cp's OEIS Frontend

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.

%I A190591 #17 Jun 28 2021 08:53:56
%S A190591 0,1,1,1,1,2,4,7,12,23,47,96,195,402,843,1781,3772,8020,17143,36810,
%T A190591 79304,171368,371450,807516,1760145,3845770,8421528,18480552,40634154,
%U A190591 89507024,197496651,436469232,966043263,2141158866,4751978668
%N 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.
%H A190591 Alois P. Heinz, <a href="/A190591/b190591.txt">Table of n, a(n) for n = 0..750</a>
%H A190591 S. Gao and H. Niederhausen, <a href="http://math.fau.edu/Niederhausen/HTML/Papers/Sequences%20Arising%20From%20Prudent%20Self-Avoiding%20Walks-February%2001-2010.pdf">Sequences Arising From Prudent Self-Avoiding Walks</a>, 2010.
%p A190591 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):
%p A190591 a:= n-> coeff(series(s, t, n+1), t, n):
%p A190591 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jun 03 2011
%K A190591 nonn
%O A190591 0,6
%A A190591 This sequence was derived by Dr. Aaron Meyerowitz and submitted by _Shanzhen Gao_, May 13 2011