OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..250
Index entries for linear recurrences with constant coefficients, signature (71,7585,-36991,-128).
FORMULA
G.f.: (1-62*x-1773*x^2+1042*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+1,7*k+1).
a(n) = (1/2) * Sum_{k=0..n} binomial(7*n+2,7*k+1).
MATHEMATICA
Table[Sum[Binomial[7*n+1, 7*k], {k, 0, n}], {n, 0, 16}] (* Vincenzo Librandi, Sep 11 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(7*n+1, 7*k));
(Magma) [&+[Binomial(7*n+1, 7*k): k in [0..n]]: n in [0..19]]; // Vincenzo Librandi, Sep 11 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 09 2025
STATUS
approved
