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

Author

Paul D. Hanna, Oct 21 2004

Keywords

• nonn
• easy
• changed

Links

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

Crossrefs

Cf. A099512.

Programs

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 *)

PARI

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

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). - Harvey P. Dale, Jul 12 2011