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.

1, 4, 15, 50, 160, 496, 1509, 4530, 13475, 39820, 117117, 343278, 1003665, 2929200, 8537910, 24863724, 72363951, 210532540, 612398025, 1781252110, 5181318054, 15073505216, 43860668800, 127657036000, 371654416575, 1082359229796

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Crossrefs

First differences of A005324. Cf. A001006, A026125.

Cf. A025117

Formula

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

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