A099623 Sum C(n-k,k+2)2^(n-k-2)(3/2)^k, k=0..floor(n/2).

0, 0, 1, 6, 27, 104, 369, 1242, 4039, 12828, 40077, 123758, 379011, 1153872, 3498025, 10572354, 31884543, 96010436, 288788613, 867967830, 2607282235, 7828953720, 23501774241, 70536546986, 211674885687, 635160738924, 1905765565309

Offset

0,4

Comments

In general a(n)=sum{k=0..floor(n/2), C(n-k,k+2)u^(n-k-2)(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n)=3u*a(n-1)-(3u^2-v)a(n-2)+(u^3-2uv)a(n-3)+u^2^v*a(n-4).

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (6,-9,-4,12).

Formula

G.f.: x^2/((1-2x)^2(1-2x-3x^2)); a(n)=6a(n-1)-9a(n-2)-4a(n-3)+12a(n-4).

a(n) = -(n/3+7/9)*2^n +(-1)^n/36 +3^(n+1)/4 . - R. J. Mathar, Dec 16 2024

Mathematica

LinearRecurrence[{6, -9, -4, 12}, {0, 0, 1, 6}, 30] (* Harvey P. Dale, Mar 27 2016 *)

Crossrefs

Sequence in context: A054457 A000395 A005325 * A119852 A220529 A027471

Adjacent sequences: A099620 A099621 A099622 * A099624 A099625 A099626

Keyword

easy,nonn,changed

Author

Paul Barry, Oct 25 2004

Status

approved