A026126 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.

1, 4, 16, 56, 188, 608, 1922, 5972, 18326, 55704, 168090, 504348, 1506531, 4484208, 13309572, 39414568, 116508361, 343890196, 1013840836, 2986129168, 8788591801, 25850576024, 76000747820, 223361900840, 656270632875, 1927845012756

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Formula

G.f.: z^4(1-z)^2M^6, with M the g.f. of the Motzkin numbers (A001006).

Second differences of A005325.

Conjecture: -(n+8)*(n-4)*a(n) +(4*n^2+5*n-73)*a(n-1) +(-2*n^2+13*n+38)*a(n-2) -(4*n+5)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jun 10 2013

Extensions

Corrected by Ralf Stephan, Apr 06 2004