A026026 - OEIS

A026026

a(n) = number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2n-1) = 4. Also a(n) = T(2n-1,n-1), where T is defined in A026022.

%I #9 Jun 23 2013 07:52:05

%S 1,3,10,35,125,451,1638,5980,21930,80750,298452,1106921,4118725,

%T 15371475,57528750,215867880,811985790,3061229850,11565545100,

%U 43782423750,166051490514,630877833102,2400830868860,9150602070760,34927775872500,133502608167292

%N a(n) = number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2n-1) = 4. Also a(n) = T(2n-1,n-1), where T is defined in A026022.

%F Expansion of (1+x^2*C^4)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

%F Conjecture: -(n+3)*(11*n-38)*a(n) +2*(35*n^2-86*n-102)*a(n-1) -4*(13*n-30)*(2*n-5)*a(n-2)=0. - _R. J. Mathar_, Jun 22 2013

%K nonn

%O 2,2

%A _Clark Kimberling_

%E Definition corrected by _Herbert Kociemba_, May 02 2004