A026270 Number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1 = s(n), |s(i) - s(i-1)| <= 1 for i >= 2, |s(2) - s(1)| = 1, |s(3) - s(2)| = 1 if s(2) = 1. Also T(n,n-1), where T is the array in A026268.

1, 2, 6, 15, 39, 102, 270, 721, 1941, 5262, 14354, 39372, 108528, 300482, 835278, 2330334, 6522882, 18313542, 51559506, 145530291, 411738723, 1167450066, 3316925794, 9441771081, 26923831029, 76901809810, 219992462862, 630245628681, 1808029517585

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

First differences of A026269. Pairwise sums of A026122.

Formula

G.f.: -1 + 4z^2(1-z)(1-z^2)/[1-z+sqrt(1-2z-3z^2)]^2.

Conjecture: (n+3)*a(n) +3*(-n-1)*a(n-1) +(-n-1)*a(n-2) +3*(n-5)*a(n-3)=0. - R. J. Mathar, Jun 23 2013