A026110 - OEIS

A026110

a(n) = 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) = 4, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array defined in A026105.

%I #14 Aug 27 2022 03:11:12

%S 1,4,15,50,160,496,1509,4530,13475,39820,117117,343278,1003665,

%T 2929200,8537910,24863724,72363951,210532540,612398025,1781252110,

%U 5181318054,15073505216,43860668800,127657036000,371654416575,1082359229796

%N a(n) = 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) = 4, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array defined in A026105.

%C Apparently the Motzkin transform of the 6th row of A025117, i.e., of 1, 4, 11, 20, ..., 11, 4, 1 followed by zeros. - _R. J. Mathar_, Dec 11 2008

%F G.f.: z(1-z)M^5, with M the g.f. of the Motzkin numbers (A001006).

%F Conjecture: -(n+6)*(n-4)*a(n) +(4*n^2-n-51)*a(n-1) +(-2*n^2+11*n+18)*a(n-2) -(4*n-1)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - _R. J. Mathar_, Jun 23 2013

%Y First differences of A005324. Cf. A001006, A026125.

%Y Cf. A025117

%K nonn

%O 4,2

%A _Clark Kimberling_