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A350144
a(n) = Sum_{k=1..n} floor(n/(2*k-1))^3.
3
1, 8, 28, 65, 127, 225, 353, 522, 759, 1037, 1369, 1803, 2273, 2827, 3539, 4260, 5078, 6095, 7123, 8301, 9709, 11103, 12623, 14449, 16312, 18270, 20614, 22920, 25358, 28338, 31130, 34107, 37627, 41001, 44761, 48976, 52974, 57200, 62136, 66986, 71908, 77720, 83140, 88854
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1..n} Sum_{d|k, k/d odd} 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[Floor[n/(2*k - 1)]^3, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Dec 17 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (n\(2*k-1))^3);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, k/d%2*(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
Column 3 of A350122.
Cf. A007331.
Sequence in context: A007259 A134747 A083013 * A028553 A100182 A321237
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 16 2021
STATUS
approved