A387484 a(n) = Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(k,n-3*k)^2.
1, 0, 0, 4, 8, 0, 16, 128, 64, 64, 1152, 2304, 768, 8192, 36864, 33792, 55296, 409600, 823296, 704512, 3719168, 13123584, 16351232, 33619968, 160890880, 329515008, 436731904, 1695809536, 5182586880, 7935623168, 18086887424, 67335356416, 141687783424
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Programs
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Magma
[(&+[2^(n-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^(n-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^(n-k)*binomial(k, n-3*k)^2);
Formula
G.f.: 1/sqrt((1-4*x^3-8*x^4)^2 - 128*x^7).