A387626 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k).
1, 1, 1, 1, 7, 21, 43, 73, 131, 297, 715, 1593, 3259, 6553, 13723, 29833, 64827, 137881, 289179, 608329, 1293083, 2762457, 5885179, 12478601, 26418363, 56028761, 119072987, 253139017, 537620571, 1140840793, 2420927291, 5139947401, 10916332411, 23182447833
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,4,4,0,0,-4).
Programs
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Magma
[&+[2^k* Binomial(2*n-6*k+1, 2*k): k in [0..Floor (n/4)]]: n in [0..35]]; // Vincenzo Librandi, Sep 04 2025
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Mathematica
Table[Sum[2^k*Binomial[2*n-6*k+1,2*k],{k,0,Floor[n/4]}],{n,0,40}] (* Vincenzo Librandi, Sep 04 2025 *) -
PARI
a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+1, 2*k));
Formula
G.f.: (1-x+2*x^4)/((1-x+2*x^4)^2 - 8*x^4).
a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).