A387604 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 3^(n-2*k) * binomial(2*n-4*k+2,2*k+1).
1, 6, 27, 114, 495, 2214, 9990, 44982, 201933, 905526, 4061016, 18217710, 81735156, 366712272, 1645244379, 7381235808, 33115172733, 148568241906, 666539094105, 2990373257970, 13416063062094, 60190050847500, 270037644213267, 1211501390490972, 5435300133382176
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-9,6,18,0,-9).
Programs
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Magma
[&+[3^(n-2*k)* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // Vincenzo Librandi, Sep 03 2025
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Mathematica
Table[Sum[3^(n-2*k)*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 03 2025 *) -
PARI
a(n) = sum(k=0, n\3, 3^(n-2*k)*binomial(2*n-4*k+2, 2*k+1))/2;
Formula
G.f.: B(x)^2, where B(x) is the g.f. of A387513.
G.f.: 1/((1-3*x-3*x^3)^2 - 36*x^4).
a(n) = 6*a(n-1) - 9*a(n-2) + 6*a(n-3) + 18*a(n-4) - 9*a(n-6).