A329970 a(n) = (-1)^(n + 1) * n * ceiling(n/2) + Sum_{k=1..n} (-1)^k * k^2 * floor(n/k).

0, 0, -2, 3, 0, -3, -7, 16, 2, -15, -21, 31, 24, -15, -57, 34, 25, -17, -27, 77, 8, -99, -111, 155, 117, -36, -140, 40, 25, -80, -96, 259, 112, -157, -249, 202, 183, -156, -354, 224, 203, -40, -62, 342, -21, -524, -548, 562, 488, -34, -358, 194, 167, -262

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

a(n) = Sum_{k=1..n} (-1)^(k + 1) * (n mod k) * k.

Mathematica

Table[(-1)^(n + 1) n Ceiling[n/2] + Sum[(-1)^k k^2 Floor[n/k], {k, 1, n}], {n, 1, 54}]
nmax = 54; CoefficientList[Series[x (1 - x + 2 x^2)/((1 - x)^2 (1 + x)^3) + 1/(1 - x) Sum[(-1)^k k^2 x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[Sum[(-1)^(k + 1) Mod[n, k] k, {k, 1, n}], {n, 1, 54}]

Prog

(PARI) a(n) = (-1)^(n + 1)*n*ceil(n/2) + sum(k=1, n, (-1)^k * k^2 * (n\k)); \\ Michel Marcus, Sep 20 2021

Crossrefs

Cf. A004125, A051126, A093005, A154585, A309176.

Sequence in context: A331781 A187988 A035549 * A245255 A180188 A316607

Adjacent sequences: A329967 A329968 A329969 * A329971 A329972 A329973

Keyword

sign

Author

Ilya Gutkovskiy, Nov 26 2019

Status

approved