A099513 Row sums of triangle A099512, so that a(n) = Sum_{k=0..n} coefficient of z^k in (1 + 3*z + z^2)^(n-[k/2]), where [k/2] is the integer floor of k/2.

1, 4, 8, 27, 89, 257, 784, 2421, 7336, 22324, 68147, 207549, 632177, 1926608, 5870089, 17884476, 54493120, 166034731, 505883825, 1541369745, 4696373312, 14309268413, 43598614528, 132839740908, 404746601923, 1233213978037

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (2, 1, 7, -1).

Formula

G.f.: (1+2*x-x^2)/(1-2*x-x^2-7*x^3+x^4).

a(0)=1, a(1)=4, a(2)=8, a(3)=27, a(n)=2*a(n-1)+a(n-2)+7*a(n-3)- a(n-4) [From Harvey P. Dale, Jul 12 2011]

Mathematica

LinearRecurrence[{2, 1, 7, -1}, {1, 4, 8, 27}, 30] (* or *) CoefficientList[ Series[ (1+2x-x^2)/(1-2x-x^2-7x^3+x^4), {x, 0, 30}], x] (* Harvey P. Dale, Jul 12 2011 *)

Prog

(PARI) a(n)=sum(k=0, n, polcoeff((1+3*x+x^2+x*O(x^k))^(n-k\2), k))

Crossrefs

Cf. A099512.

Sequence in context: A026085 A036720 A110132 * A104042 A338429 A117864

Adjacent sequences: A099510 A099511 A099512 * A099514 A099515 A099516

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2004

Status

approved