A387622 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k,2*k).
1, 1, 1, 3, 13, 31, 61, 151, 413, 1031, 2445, 5991, 15069, 37447, 91917, 226503, 561373, 1389735, 3431501, 8474983, 20955229, 51814407, 128054029, 316455559, 782209629, 1933537511, 4779082829, 11812031271, 29195752157, 72164132167, 178368130061
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,4,4,0,-4).
Programs
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Magma
[&+[2^k* Binomial(2*n-4*k, 2*k): k in [0..Floor (n/3)]]: n in [0..30]]; // Vincenzo Librandi, Sep 05 2025
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Mathematica
Table[Sum[2^k*Binomial[2*n-4*k,2*k],{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 05 2025 *) -
PARI
a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k, 2*k));
Formula
G.f.: (1-x-2*x^3)/((1-x-2*x^3)^2 - 8*x^4).
a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).