A387650 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+1,2*n-6*k).
1, 0, 0, 1, 6, 0, 1, 20, 20, 1, 42, 140, 57, 72, 504, 673, 254, 1320, 3697, 2796, 3212, 13729, 20802, 14612, 40873, 103232, 105616, 128129, 391222, 637840, 613089, 1296772, 2984388, 3658945, 4744730, 11570396, 19628825, 22729464, 41870056, 88630753, 121927726, 167430712
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1500
- Index entries for linear recurrences with constant coefficients, signature (0,0,2,4,0,-1,4,-4).
Programs
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Magma
[&+[2^(n-3*k)* Binomial(2*k+1, 2*n-6*k): k in [0..Floor (n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 06 2025
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Mathematica
Table[Sum[2^(n-3*k)*Binomial[2*k+1,2*n-6*k],{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 06 2025 *) -
PARI
a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+1, 2*n-6*k));
Formula
G.f.: (1-x^3+2*x^4)/((1-x^3+2*x^4)^2 - 8*x^4).
a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).