A190591 The coefficient of t^n in the power series solution of u in the equation -t+(1-t+t^2+t^3)*u-(t+t^4)*u^2+(t^3+t^5)*u^3-t^4*u^4=0.

0, 1, 1, 1, 1, 2, 4, 7, 12, 23, 47, 96, 195, 402, 843, 1781, 3772, 8020, 17143, 36810, 79304, 171368, 371450, 807516, 1760145, 3845770, 8421528, 18480552, 40634154, 89507024, 197496651, 436469232, 966043263, 2141158866, 4751978668

Offset: 0

Author

This sequence was derived by Dr. Aaron Meyerowitz and submitted by Shanzhen Gao, May 13 2011

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750
• S. Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, 2010.

Programs

Maple

s:= solve(-t+(1-t+t^2+t^3)*u-(t+t^4)*u^2+(t^3+t^5)*u^3-t^4*u^4, u):
a:= n-> coeff(series(s, t, n+1), t, n):
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 03 2011