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