A387513 a(n) = Sum_{k=0..floor(n/3)} 3^(n-2*k) * binomial(n-2*k,k)^2.
1, 3, 9, 30, 117, 486, 2034, 8505, 35721, 151173, 644274, 2760237, 11871846, 51223428, 221624019, 961221735, 4177946385, 18193784220, 79361528679, 346693615128, 1516579388406, 6642203294691, 29123170761807, 127821123780795, 561522735794574, 2468882933230887
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
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Magma
[(&+[3^(n-2*k) * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025
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Mathematica
Table[Sum[3^(n-2*k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* Vincenzo Librandi, Sep 01 2025 *) -
PARI
a(n) = sum(k=0, n\3, 3^(n-2*k)*binomial(n-2*k, k)^2);
Formula
G.f.: 1/sqrt((1-3*x-3*x^3)^2 - 36*x^4).