OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (5,5,145,55,8).
FORMULA
G.f.: (1-4*x+12*x^2-6*x^3-6*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+1, 5*k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Sep 14 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(3*n+1, 5*k));
(Magma) [&+[Binomial(3*n+1, 5*k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 14 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 10 2025
STATUS
approved