A366395 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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));