A099511 Row sums of triangle A099510, so that a(n) = Sum_{k=0..n} coefficient of z^k in (1 + 2*z + z^2)^(n-[k/2]), where [k/2] is the integer floor of k/2.

1, 3, 6, 17, 45, 116, 305, 799, 2090, 5473, 14329, 37512, 98209, 257115, 673134, 1762289, 4613733, 12078908, 31622993, 82790071, 216747218, 567451585, 1485607537, 3889371024, 10182505537, 26658145587, 69791931222, 182717648081

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: (1+x-x^2)/(1-2*x-x^2-2*x^3+x^4). a(n) = Sum_{k=0..n} binomial(2*n-2*[k/2], k).

Prog

(PARI) a(n)=sum(k=0, n, polcoeff((1+2*x+x^2+x*O(x^k))^(n-k\2), k))

Crossrefs

Cf. A099510.

Sequence in context: A237670 A321227 A006081 * A204517 A307685 A360273

Adjacent sequences: A099508 A099509 A099510 * A099512 A099513 A099514

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2004

Status

approved