A026123 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 2, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is the array in A026120; a(n) = U(n,n+1), where U is the array in A026148.

1, 4, 10, 28, 76, 209, 575, 1589, 4405, 12253, 34189, 95679, 268503, 755457, 2130717, 6023235, 17063139, 48434514, 137741280, 392407134, 1119766942, 3200326627, 9160055809, 26254474379, 75348899051, 216515177336, 622887159274

Offset

2,2

Links

Table of n, a(n) for n=2..28.

Formula

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

D-finite with recurrence: (n+5)*a(n) +5*(-n-3)*a(n-1) +(5*n+1)*a(n-2) +(5*n+3)*a(n-3) +6*(-n+3)*a(n-4)=0. - R. J. Mathar, Jun 23 2013

Crossrefs

First differences of A026134.

Sequence in context: A348057 A121302 A026150 * A091468 A103457 A377100

Adjacent sequences: A026120 A026121 A026122 * A026124 A026125 A026126

Keyword

nonn

Author

Clark Kimberling

Status

approved