A387038 a(n) = Sum_{k=0..n} binomial(3*n+2,5*k).

1, 2, 57, 474, 3004, 25773, 215766, 1669801, 13333932, 107746282, 859595529, 6863694378, 54986385093, 439924466026, 3517929664756, 28146676447417, 225191238869774, 1801425114687749, 14411355379952868, 115292842751246298, 922338323835136341

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,5,145,55,8).

Formula

G.f.: (1-3*x+42*x^2+34*x^3+4*x^4)/((1-8*x) * (1+3*x+19*x^2+7*x^3+x^4)).

a(n) = 5*a(n-1) + 5*a(n-2) + 145*a(n-3) + 55*a(n-4) + 8*a(n-5) for n > 4.

Mathematica

Table[Sum[Binomial[3*n+2, 5*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Oct 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n+2, 5*k));
(Magma) [&+[Binomial(3*n+2, 5*k) : k in [0..n] ]: n in [0..40]]; // Vincenzo Librandi, Oct 16 2025

Crossrefs

Cf. A387872.

Sequence in context: A245783 A189057 A229015 * A324318 A058196 A024237

Adjacent sequences: A387035 A387036 A387037 * A387039 A387040 A387041

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 12 2025

Status

approved