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.
1, 5, 21, 83, 319, 1209, 4550, 17068, 63954, 239666, 898909, 3375825, 12697035, 47833905, 180510210, 682341000, 2583591150, 9798281910, 37218303330, 141585223494, 539395269462, 2057771255210, 7860697923436, 30065829471048, 115135255095140, 441410428339972
Offset: 2
Keywords
Crossrefs
First differences of A003517.
Formula
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.
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