A387629 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k+1).
1, 3, 5, 7, 11, 31, 83, 183, 351, 675, 1435, 3231, 7119, 14987, 30963, 64871, 138775, 298403, 636091, 1344191, 2838399, 6021371, 12818467, 27277207, 57911207, 122790675, 260485131, 553185519, 1175285967, 2496108459, 5298760307, 11246985927, 23877452663, 50702334403
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,4,4,0,0,-4).
Programs
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Magma
[&+[2^k* Binomial(2*n-6*k+1, 2*k+1): k in [0..Floor (n/4)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025
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Mathematica
Table[Sum[2^k*Binomial[2*n-6*k+1,2*k+1],{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 04 2025 *) -
PARI
a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+1, 2*k+1));
Formula
G.f.: (1+x-2*x^4)/((1+x-2*x^4)^2 - 4*x).
a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).