A390485 a(n) = Sum_{k=0..floor(n/3)} (4*k+1) * binomial(3*n-5*k+1,n-3*k)/(3*n-5*k+1).

1, 1, 3, 13, 60, 298, 1559, 8461, 47202, 269029, 1559793, 9170721, 54549314, 327673535, 1984930805, 12111852548, 74377027931, 459306563146, 2850555663397, 17770113357840, 111221824374360, 698654228215989, 4403147211571834, 27833498346280446, 176427713240974409

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: g/(1-x^3*g^4) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(4*k+1)*Binomial[3*n-5*k+1, n-3*k]/(3*n-5*k+1), {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, Nov 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (4*k+1)*binomial(3*n-5*k+1, n-3*k)/(3*n-5*k+1));
(Magma) [&+[(4*k+1)*Binomial(3*n-5*k+1, n-3*k)/(3*n-5*k+1): k in [0..Floor(n/3)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A109957, A390486.

Cf. A001764.

Sequence in context: A391459 A386940 A199641 * A357151 A367058 A353208

Adjacent sequences: A390482 A390483 A390484 * A390486 A390487 A390488

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved