A387479 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k,n-3*k)^2.
1, 0, 0, 2, 6, 0, 4, 48, 36, 8, 216, 648, 232, 768, 5184, 6944, 3696, 28800, 86464, 71712, 137376, 691328, 1185216, 1067904, 4280512, 12749952, 15523200, 26248832, 102010752, 201056256, 243856384, 694548480, 1995570432, 3031771136, 5109762048, 16129681920
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Programs
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Magma
[(&+[2^k *3^(n-3*k)* Binomial(k,n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025
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Mathematica
Table[Sum[2^k* 3^(n-3*k)*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 01 2025 *) -
PARI
a(n) = sum(k=0, n\3, 2^k*3^(n-3*k)*binomial(k, n-3*k)^2);
Formula
G.f.: 1/sqrt((1-2*x^3-6*x^4)^2 - 48*x^7).