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A366395
a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+2,3).
5
1, 3, 10, 16, 32, 49, 78, 100, 152, 194, 261, 318, 410, 489, 631, 717, 871, 1014, 1205, 1351, 1617, 1806, 2083, 2300, 2641, 2903, 3333, 3612, 4048, 4450, 4947, 5289, 5923, 6367, 7041, 7548, 8252, 8805, 9683, 10245, 11107, 11873, 12820, 13497, 14719, 15526, 16655
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1..n} binomial(k+1,2) * (floor(n/k) mod 2).
G.f.: -1/(1-x) * Sum_{k>=1} (-x)^k/(1-x^k)^3 = 1/(1-x) * Sum_{k>=1} binomial(k+1,2) * x^k/(1+x^k).
MATHEMATICA
Array[Sum[(-1)^(k - 1)*Binomial[Floor[#/k] + 2, 3], {k, #}] &, 56] (* Michael De Vlieger, Oct 25 2023 *)
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(k-1)*binomial(n\k+2, 3));
CROSSREFS
Partial sums of A365007.
Cf. A364970.
Sequence in context: A063109 A083684 A141497 * A059911 A160375 A300017
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 24 2023
STATUS
approved