A391062 Expansion of g/(1 - x^3*g^3), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 3, 13, 59, 291, 1517, 8214, 45753, 260487, 1509065, 8867109, 52718507, 316556760, 1917000798, 11694375261, 71798007603, 443299413315, 2750780802501, 17145791247473, 107301436799937, 673956814783616, 4247098354171151, 26844822672426135, 170147997400300661, 1081171606752158598

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (3*k+1) * binomial(3*n-6*k+1,n-3*k)/(3*n-6*k+1).

Mathematica

Table[Sum[(3*k+1)*Binomial[3*n-6*k+1, n-3*k]/(3*n-6*k+1), {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 01 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k+1)*binomial(3*n-6*k+1, n-3*k)/(3*n-6*k+1));
(Magma) [&+[(3*k+1)*Binomial(3*n-6*k+1, n-3*k)/(3*n-6*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Dec 01 2025

Crossrefs

Cf. A390485, A391059, A391061, A391063, A391064, A391065.

Cf. A001764.

Sequence in context: A151233 A151234 A330799 * A379159 A367057 A317776

Adjacent sequences: A391059 A391060 A391061 * A391063 A391064 A391065

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2025

Status

approved