cp's OEIS Frontend

A026126 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.

%I A026126 #8 Jun 10 2013 04:40:08
%S A026126 1,4,16,56,188,608,1922,5972,18326,55704,168090,504348,1506531,
%T A026126 4484208,13309572,39414568,116508361,343890196,1013840836,2986129168,
%U A026126 8788591801,25850576024,76000747820,223361900840,656270632875,1927845012756
%N A026126 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.
%F A026126 G.f.: z^4(1-z)^2M^6, with M the g.f. of the Motzkin numbers (A001006).
%F A026126 Second differences of A005325.
%F A026126 Conjecture: -(n+8)*(n-4)*a(n) +(4*n^2+5*n-73)*a(n-1) +(-2*n^2+13*n+38)*a(n-2) -(4*n+5)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - _R. J. Mathar_, Jun 10 2013
%K A026126 nonn
%O A026126 4,2
%A A026126 _Clark Kimberling_
%E A026126 Corrected by _Ralf Stephan_, Apr 06 2004