read `Motzkin.txt`:

print(`Here are examples with restrictions on run lengths`):
print(``):
print(``):
print(``):

print(`Let a(n) be the number of Motzkin paths of length n`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{},{},{},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):



print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1},{},{},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):


print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1,2}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1,2},{},{},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):


print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No downward run can have length in {1,2}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{},{1,2},{},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No flat run can have length in {1}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{},{},{1},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No flat run can have length in {1,2}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{},{},{1,2},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1} and no flat run can have length in {1}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1},{},{1},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1,2} and no flat run can have length in {1}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1,2},{},{1},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1} and no flat run can have length in {1,2}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1},{},{1,2},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1,2} and no flat run can have length in {1,2}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1,2},{},{1,2},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):



print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1}, no downward run can have length in {1}, and no flat run can have length {1}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1},{1},{1},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):


print(``): print(``): print(`----------------------------`): print(``): print(``):

print(`Let a(n) be the number of Motzkin paths of length n with the following restrictions`):
print(`No upward run can have length in {1}, no downward run can have length in {2,4}, and no flat run can have length {3,6,9}`):
print(`The generating function P(x) of the sequence a(n) satisfies the algebraic equation`):
L:=SeqABCDE({},{},{1},{2,4},{3,6,9},100):
eq:= Aeq(L,x,P):
if eq=FAIL then 
  print(eq):
  print(`Cannot find the equation from the first 101 terms of the sequence`):
else 
  print(eq=0):
fi:
print(``):
print(``):
print(`Here are the terms a(n) from n=0 to n=100`):
print(``):
print(L):

print(``): print(``): print(`----------------------------`): print(``): print(``):