A390703 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-3*k+1,n-3*k).

1, 4, 21, 121, 725, 4446, 27693, 174436, 1108080, 7085541, 45548877, 294085065, 1905673810, 12386964125, 80729648541, 527353208457, 3451811268203, 22634323680339, 148654460310396, 977702029182141, 6438609795731778, 42450443171333517, 280176360105499197, 1850974170436888686, 12239233077527460321

Offset

0,2

Links

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

Formula

a(n) = [x^n] 1/((1-x^3) * (1-x)^(2*n+2)).

a(n) = Sum_{k=0..n} (-3)^k * binomial(3*n+k+4,n-k).

Mathematica

Table[Sum[(-3)^k*Binomial[3*n +k+4, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(3*n-3*k+1, n-3*k));
(Magma) [&+[(-3)^k*Binomial(3*n+k+4, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A001840, A390702, A390704.

Sequence in context: A046090 A045721 A101810 * A371774 A274969 A236525

Adjacent sequences: A390700 A390701 A390702 * A390704 A390705 A390706

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved