A387624 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k).
1, 1, 7, 21, 63, 213, 671, 2149, 6911, 22101, 70847, 227045, 727391, 2330901, 7468767, 23931621, 76683583, 245713493, 787329151, 2522806629, 8083720351, 25902323221, 82997717407, 265946059365, 852159682431, 2730539119701, 8749350654527, 28035173160421
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,3,4,-4).
Programs
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Magma
[&+[2^k* Binomial(2*n-2*k+1, 2*k): k in [0..Floor (n/2)]]: n in [0..30]]; // Vincenzo Librandi, Sep 04 2025
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Mathematica
Table[Sum[2^k*Binomial[2*n-2*k+1,2*k],{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 04 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^k*binomial(2*n-2*k+1, 2*k));
Formula
G.f.: (1-x+2*x^2)/((1-x+2*x^2)^2 - 8*x^2).
a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).