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.

1, 3, 10, 35, 125, 451, 1638, 5980, 21930, 80750, 298452, 1106921, 4118725, 15371475, 57528750, 215867880, 811985790, 3061229850, 11565545100, 43782423750, 166051490514, 630877833102, 2400830868860, 9150602070760, 34927775872500, 133502608167292

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Formula

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.

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

Extensions

Definition corrected by Herbert Kociemba, May 02 2004