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A390412
a(n) = Sum_{k=0..n} binomial(n+3*k+1,k).
8
1, 6, 43, 339, 2808, 23940, 207959, 1830287, 16265389, 145627687, 1311563670, 11869173033, 107840128270, 983098021418, 8987876609049, 82374355902918, 756597255784231, 6962465128795836, 64179099198994169, 592486203654560853, 5477098529707573913
OFFSET
0,2
LINKS
FORMULA
G.f.: g/((1-4*x*g^3) * (1-x*g)) where g = 1+x*g^4 is the g.f. of A002293.
MATHEMATICA
Table[Sum[Binomial[n+3*k+1, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 06 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+3*k+1, k));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 04 2025
STATUS
approved