A100135 - OEIS

A100135

a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^k.

1, 1, 1, 1, 1, 1, 3, 9, 21, 41, 71, 113, 173, 269, 443, 777, 1413, 2577, 4615, 8065, 13813, 23413, 39691, 67801, 116973, 203337, 354519, 617345, 1071197, 1851677, 3192731, 5501033, 9485621, 16381185, 28330119, 49035777, 84883621, 146875717, 253983307, 438968761

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OFFSET

0,7

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,2).

FORMULA

G.f.: (1-x)^2/((1-x)^3 - 2*x^6).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 2*a(n-6).

MATHEMATICA

LinearRecurrence[{3, -3, 1, 0, 0, 2}, {1, 1, 1, 1, 1, 1}, 38] (* James C. McMahon, Dec 22 2023 *)

CROSSREFS