cp's OEIS Frontend

A026017 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) = 2, s(2n-1) = 5. Also a(n) = T(2n-1,n-2), where T is the array defined in A026009.

%I A026017 #6 Jun 20 2013 16:23:25
%S A026017 1,5,21,83,319,1209,4550,17068,63954,239666,898909,3375825,12697035,
%T A026017 47833905,180510210,682341000,2583591150,9798281910,37218303330,
%U A026017 141585223494,539395269462,2057771255210,7860697923436,30065829471048,115135255095140,441410428339972
%N A026017 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) = 2, s(2n-1) = 5. Also a(n) = T(2n-1,n-2), where T is the array defined in A026009.
%F A026017 Expansion of (1+x^1*C^3)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F A026017 Conjecture: (n+4)*a(n) +(-8*n-17)*a(n-1) +(19*n+1)*a(n-2) +6*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Jun 20 2013
%Y A026017 First differences of A003517.
%K A026017 nonn
%O A026017 2,2
%A A026017 _Clark Kimberling_