A366395 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+2,3).

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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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. A078471, A366659, A366723.

Cf. A364970.

Sequence in context: A063109 A083684 A141497 * A059911 A160375 A300017

Adjacent sequences: A366392 A366393 A366394 * A366396 A366397 A366398

Keyword

nonn

Author

Seiichi Manyama, Oct 24 2023

Status

approved