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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.
3
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
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.
Sequence in context: A301973 A132308 A372015 * A056327 A026328 A014532
KEYWORD
nonn
STATUS
approved