cp's OEIS Frontend

A026288 Number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, s(1) = 1, s(n) = 2, |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-2), where T is the array in A026268.

%I A026288 #8 Jul 08 2022 10:52:43
%S A026288 1,2,5,14,38,104,285,784,2164,5994,16658,46442,129868,364182,1023960,
%T A026288 2886174,8153952,23086374,65497653,186175794,530148414,1512174076,
%U A026288 4320093569,12360382436,35414530188,101603373430,291864076387,839402336610
%N A026288 Number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, s(1) = 1, s(n) = 2, |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-2), where T is the array in A026268.
%F A026288 G.f.: 8z^2(1-z)(1-z^2)/[1-z+sqrt(1-2z-3z^2)]^3.
%F A026288 D-finite with recurrence: (n+4)*a(n) +(-5*n-11)*a(n-1) +(5*n+2)*a(n-2) +(5*n-13)*a(n-3) +6*(-n+5)*a(n-4)=0. - _R. J. Mathar_, Jun 23 2013
%Y A026288 Pairwise sums of A026123.
%K A026288 nonn
%O A026288 2,2
%A A026288 _Clark Kimberling_