cp's OEIS Frontend

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.

%I A026270 #6 Jun 23 2013 11:24:40
%S A026270 1,2,6,15,39,102,270,721,1941,5262,14354,39372,108528,300482,835278,
%T A026270 2330334,6522882,18313542,51559506,145530291,411738723,1167450066,
%U A026270 3316925794,9441771081,26923831029,76901809810,219992462862,630245628681,1808029517585
%N 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.
%F A026270 G.f.: -1 + 4z^2(1-z)(1-z^2)/[1-z+sqrt(1-2z-3z^2)]^2.
%F A026270 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
%Y A026270 First differences of A026269. Pairwise sums of A026122.
%K A026270 nonn
%O A026270 2,2
%A A026270 _Clark Kimberling_