A366938 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(k+2,3) * floor(n/k).

1, -2, 9, -14, 22, -27, 58, -85, 91, -97, 190, -243, 213, -266, 460, -499, 471, -553, 778, -970, 896, -845, 1456, -1697, 1264, -1560, 2270, -2289, 2207, -2307, 3150, -3793, 3049, -3125, 4765, -5079, 4061, -4492, 6634, -6714, 5628, -6370, 7821, -9120, 7986, -7013

Offset

1,2

Links

Table of n, a(n) for n=1..46.

Formula

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).

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(k-1)*binomial(k+2, 3)*(n\k));
(Python)
from math import isqrt
def A366938(n): return (((s:=isqrt(m:=n>>1))*(s+1)**3*(s+2)<<4)-(t:=isqrt(n))*(t+1)**2*(t+2)*(t+3)-sum((((q:=m//w)+1)*(q*(q+1)*(q+2)+(w*(w+1)*((w<<1)+1)<<1))<<4) for w in range(1, s+1))+sum(((q:=n//w)+1)*(q*(q+2)*(q+3)+(w*(w+1)*(w+2)<<2)) for w in range(1, t+1)))//24 # Chai Wah Wu, Oct 29 2023

Crossrefs

Partial sums of A320901.

Cf. A024919, A366937, A366939.

Cf. A365409, A366659.

Sequence in context: A242466 A071344 A224855 * A254608 A324275 A106360

Adjacent sequences: A366935 A366936 A366937 * A366939 A366940 A366941

Keyword

sign

Author

Seiichi Manyama, Oct 29 2023

Status

approved