A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k+1).
1, 3, 7, 27, 83, 263, 855, 2723, 8731, 27999, 89663, 287355, 920771, 2950263, 9453607, 30291667, 97062123, 311012623, 996563855, 3193247403, 10231988371, 32785923879, 105054547063, 336621829635, 1078623042491, 3456186066623, 11074510391007, 35485583833307
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+1): k in [0..Floor (n/2)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025
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Mathematica
Table[Sum[2^k*Binomial[2*n-2*k+1,2*k+1],{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+1));
Formula
G.f.: (1+x-2*x^2)/((1+x-2*x^2)^2 - 4*x).
a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).