A366659 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+3,4).

1, 4, 15, 30, 66, 115, 200, 295, 471, 659, 946, 1259, 1715, 2194, 2920, 3591, 4561, 5585, 6916, 8216, 10082, 11823, 14124, 16389, 19350, 22174, 26004, 29435, 33931, 38445, 43902, 48925, 55767, 61941, 69831, 77275, 86415, 94968, 106094, 115874, 128216, 140214, 154405

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+2,3) * (floor(n/k) mod 2).

G.f.: -1/(1-x) * Sum_{k>=1} (-x)^k/(1-x^k)^4 = 1/(1-x) * Sum_{k>=1} binomial(k+2,3) * x^k/(1+x^k).

Mathematica

Array[Sum[(-1)^(k - 1)*Binomial[Floor[#/k] + 3, 4], {k, #}] &, 56] (* Michael De Vlieger, Oct 25 2023 *)

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(k-1)*binomial(n\k+3, 4));

Crossrefs

Partial sums of A366813.

Cf. A078471, A366395, A366723.

Sequence in context: A349428 A188075 A322740 * A121914 A336607 A321490

Adjacent sequences: A366656 A366657 A366658 * A366660 A366661 A366662

Keyword

nonn

Author

Seiichi Manyama, Oct 24 2023

Status

approved