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

4,2

Links

Table of n, a(n) for n=4..29.

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

Crossrefs

Sequence in context: A261386 A073388 A109634 * A026155 A025182 A057585

Adjacent sequences: A026123 A026124 A026125 * A026127 A026128 A026129

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected by Ralf Stephan, Apr 06 2004

Status

approved