A387849 a(n) = Sum_{k=0..n} binomial(4*n,6*k).

1, 1, 29, 926, 9829, 164921, 2973350, 43942081, 708653429, 11582386286, 182670807229, 2926800830801, 47006639297270, 750176293590361, 12005786207578829, 192222214478506046, 3074148508920116629, 49188537999608859881, 787111112023373201990, 12592752145699441737841

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (6,69,1366,1359,1296).

Formula

G.f.: (1-5*x-46*x^2-683*x^3-453*x^4-216*x^5)/((1-16*x) * (1+x+x^2) * (1+9*x+81*x^2)).

a(n) = 6*a(n-1) + 69*a(n-2) + 1366*a(n-3) + 1359*a(n-4) + 1296*a(n-5) for n > 5.

For n>0, a(n) = (2^(4*n - 1) + (9^n + 1)*cos(2*Pi*n/3))/3. - Vaclav Kotesovec, Sep 14 2025

Mathematica

Table[Sum[ Binomial[ 4*n, 6*k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Sep 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n, 6*k));
(Magma) [&+[Binomial(4*n, 6*k): k in [0..n]]: n in [0..40]]; // Vincenzo Librandi, Sep 13 2025

Crossrefs

Cf. A070967, A306847, A377627, A378031, A387850.

Sequence in context: A157877 A158665 A324432 * A167738 A107964 A096699

Adjacent sequences: A387846 A387847 A387848 * A387850 A387851 A387852

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved