A026125 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 4, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array in A026120.

1, 3, 11, 35, 110, 336, 1013, 3021, 8945, 26345, 77297, 226161, 660387, 1925535, 5608710, 16325814, 47500227, 138168589, 401865485, 1168854085, 3400065944, 9892187162, 28787163584, 83796367200, 243997380575, 710704813221, 2070833535813

Offset

3,2

Links

Table of n, a(n) for n=3..29.

Formula

G.f.: z^3(1-z)^2M^5, with M the g.f. of the Motzkin numbers (A001006).

Conjecture: -(n+7)*(n-3)*a(n) +(4*n+17)*(n-3)*a(n-1) +(-2*n^2+13*n+27)*a(n-2) -(4*n+5)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jun 23 2013

Crossrefs

First differences of A026110.

Sequence in context: A126939 A370199 A126940 * A026154 A025181 A004054

Adjacent sequences: A026122 A026123 A026124 * A026126 A026127 A026128

Keyword

nonn

Author

Clark Kimberling

Status

approved