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
Keywords
Crossrefs
First differences of A026134.
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