A387817 a(n) = Sum_{k=0..n} binomial(7*n+3,7*k+1).

3, 55, 24463, 2043275, 328589491, 37923176863, 5109310929719, 638253257115123, 82667246362298267, 10521522072173510919, 1350448850556607111519, 172629587500350499308123, 22110643039617445675165443, 2829295276817232488317262447, 362203278180843495551038466567

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..260

Index entries for linear recurrences with constant coefficients, signature (71,7585,-36991,-128).

Formula

G.f.: (3-158*x-2197*x^2+200*x^3)/((1-128*x) * (1+57*x-289*x^2-x^3)).

a(n) = 71*a(n-1) + 7585*a(n-2) - 36991*a(n-3) - 128*a(n-4).

a(n) = Sum_{k=0..n} binomial(7*n+3,7*k+2).

a(n) = (1/2) * Sum_{k=0..n} binomial(7*n+4,7*k+2).

Mathematica

Table[Sum[Binomial[7*n+3, 7*k+1], {k, 0, n}], {n, 0, 40}] (* Vincenzo Librandi, Sep 11 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(7*n+3, 7*k+1));
(Magma) [&+[Binomial(7*n+3, 7*k+1): k in [0..n]]: n in [0..19]]; // Vincenzo Librandi, Sep 11 2025

Crossrefs

Cf. A094211, A387816.

Sequence in context: A172950 A172962 A110058 * A083869 A290773 A119188

Adjacent sequences: A387814 A387815 A387816 * A387818 A387819 A387820

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 09 2025

Status

approved