A387554 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+2,2*n-4*k+1).
1, 0, 2, 4, 3, 20, 16, 56, 117, 152, 510, 700, 1671, 3532, 5772, 14480, 24761, 52400, 109114, 198324, 437899, 821828, 1670536, 3423784, 6547325, 13666184, 26654966, 53492716, 108440335, 212433276, 432672004, 857090304, 1713987777, 3452225824, 6839636530
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, 2*n-4*k+1)/2: k in [0..Floor(n/2)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025
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Mathematica
Table[Sum[2^(n-2*k)*Binomial[2*k+2, 2*n-4*k+1]/2,{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 02 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k+2, 2*n-4*k+1))/2;
Formula
G.f.: B(x)^2, where B(x) is the g.f. of A387515.
G.f.: 1/((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).