OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..700
Index entries for linear recurrences with constant coefficients, signature (3,3,4).
FORMULA
G.f.: (1-x+2*x^2)/((1-4*x) * (1+x+x^2)).
a(n) = 3*a(n-1) + 3*a(n-2) + 4*a(n-3) for n > 2.
MATHEMATICA
Table[Sum[Binomial[2*n+1, 3*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 15 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*n+1, 3*k));
(Magma) [&+[Binomial(2*n+1, 3*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 15 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 10 2025
STATUS
approved