A387647 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k,2*n-4*k).
1, 0, 1, 2, 1, 12, 5, 30, 61, 64, 281, 314, 857, 1812, 2701, 7606, 11925, 26376, 55393, 96402, 223985, 405276, 835989, 1726158, 3233133, 6901328, 13260073, 26731882, 54453001, 105630628, 217246237, 427776358, 856449221, 1729791512, 3411468145, 6904065986
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1500
- Index entries for linear recurrences with constant coefficients, signature (0,2,4,-1,4,-4).
Programs
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Magma
[&+[2^(n-2*k)* Binomial(2*k, 2*n-4*k): k in [0..Floor (n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 06 2025
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Mathematica
Table[Sum[2^(n-2*k)*Binomial[2*k,2*n-4*k],{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 06 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k, 2*n-4*k));
Formula
G.f.: (1-x^2-2*x^3)/((1-x^2-2*x^3)^2 - 8*x^5).
a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).