A366971 a(n) = Sum_{k=3..n} binomial(k,3) * floor(n/k).

0, 0, 1, 5, 15, 36, 71, 131, 216, 346, 511, 756, 1042, 1441, 1907, 2527, 3207, 4128, 5097, 6371, 7737, 9442, 11213, 13538, 15848, 18734, 21744, 25423, 29077, 33743, 38238, 43818, 49440, 56104, 62694, 70979, 78749, 88154, 97580, 108790, 119450, 132680, 145021, 159974

Offset

1,4

Links

Table of n, a(n) for n=1..44.

Formula

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

a(n) = (A064603(n) - 3*A064602(n) + 2*A024916(n))/6. - Chai Wah Wu, Oct 30 2023

Prog

(PARI) a(n) = sum(k=3, n, binomial(k, 3)*(n\k));
(Python)
from math import isqrt, comb
def A366971(n): return -comb((s:=isqrt(n))+1, 4)*(s+1)+sum(comb((q:=n//w)+1, 4)+(q+1)*comb(w, 3) for w in range(1, s+1)) # Chai Wah Wu, Oct 30 2023

Crossrefs

Partial sums of A363607.

Cf. A366968, A366969, A366970.

Cf. A024916, A064602, A064603, A366967.

Sequence in context: A105720 A174655 A184631 * A011933 A093802 A006008

Adjacent sequences: A366968 A366969 A366970 * A366972 A366973 A366974

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2023

Status

approved