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

4,2

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

Links

Table of n, a(n) for n=4..29.

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

Crossrefs

First differences of A005324. Cf. A001006, A026125.

Cf. A025117

Sequence in context: A301973 A132308 A372015 * A056327 A026328 A014532

Adjacent sequences: A026107 A026108 A026109 * A026111 A026112 A026113

Keyword

nonn

Author

Clark Kimberling

Status

approved