A387507 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n-2*k,k)^2.
1, 1, 1, 3, 9, 19, 37, 87, 217, 507, 1157, 2727, 6553, 15627, 37077, 88519, 212569, 510715, 1226853, 2952615, 7120921, 17192427, 41538293, 100458759, 243211865, 589313755, 1428931333, 3467193191, 8418640793, 20453853003, 49722339861, 120936710471
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
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Magma
[(&+[2^k * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Sep 02 2025
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Mathematica
Table[Sum[2^k*Binomial[n-2*k, k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 02 2025 *) -
PARI
a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)^2);
Formula
G.f.: 1/sqrt((1-x-2*x^3)^2 - 8*x^4).