A387478 a(n) = Sum_{k=0..floor(n/2)} 2^k * 3^(n-2*k) * binomial(k,n-2*k)^2.
1, 0, 2, 6, 4, 48, 44, 216, 664, 984, 5216, 9312, 30160, 93312, 194528, 717792, 1674688, 4842624, 14554304, 35517312, 112151680, 293213568, 823387136, 2409934848, 6348908800, 18760218624, 51418362368, 143838905856, 414017065984, 1132211048448, 3255687793664
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
-
Magma
[(&+[2^k *3^(n-2*k)* Binomial(k,n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025
-
Mathematica
Table[Sum[2^k* 3^(n-2*k)*Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 01 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^k*3^(n-2*k)*binomial(k, n-2*k)^2);
Formula
G.f.: 1/sqrt((1-2*x^2-6*x^3)^2 - 48*x^5).