OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * (d^3 - (d - 1)^3).
G.f.: (1/(1 - x)) * Sum_{k>=1} (k^3 - (k-1)^3) * x^k/(1 + x^(2*k)).
MATHEMATICA
a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^3, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Dec 18 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^3);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*(d^3-(d-1)^3)));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, (k^3-(k-1)^3)*x^k/(1+x^(2*k)))/(1-x))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 18 2021
STATUS
approved