OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (21,353,-32).
FORMULA
G.f.: (1 + 36*x + 24*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
a(n) = A139398(5*n+3).
a(n) = 2^(5*n + 4)/10 + (( 475 - 213*sqrt(5))/phi^(5*n) + ( 65 - 33*sqrt(5))*(-1)^n*phi^(5*n)) / (10*(41*sqrt(5)-90)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Jun 20 2021
MATHEMATICA
a[n_] := Sum[Binomial[5*n + 3, 5*k], {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Jun 20 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(5*n+3, 5*k));
(PARI) my(N=20, x='x+O('x^N)); Vec((1+36*x+24*x^2)/((1-32*x)*(1+11*x-x^2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 20 2021
STATUS
approved