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

2,2

Links

Table of n, a(n) for n=2..27.

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

Crossrefs

Sequence in context: A243871 A081567 A224509 * A047037 A339040 A201058

Adjacent sequences: A026023 A026024 A026025 * A026027 A026028 A026029

Keyword

nonn

Author

Clark Kimberling

Extensions

Definition corrected by Herbert Kociemba, May 02 2004

Status

approved