A307559 a(n) = floor(n/3)*(n - floor(n/3))*(n - floor(n/3) - 1).

0, 0, 2, 6, 12, 24, 40, 60, 90, 126, 168, 224, 288, 360, 450, 550, 660, 792, 936, 1092, 1274, 1470, 1680, 1920, 2176, 2448, 2754, 3078, 3420, 3800, 4200, 4620, 5082, 5566, 6072, 6624, 7200, 7800, 8450, 9126, 9828, 10584, 11368, 12180, 13050, 13950, 14880, 15872

Offset

1,3

Comments

a(n) is an upper bound for the irregularity of a graph with n vertices (see Theorem 3.2 of the Tavakoli et al. reference).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, and I. Gutman, Extremely irregular graphs, Kragujevac J. Math., 37 (1), 2013, 135-139.

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Formula

a(n) = 2*A200067(n).

G.f.: 2*x^3*(1+x)*(1+x^2) / ( (1+x+x^2)^2*(x-1)^4 ). - R. J. Mathar, Jul 22 2022

Example

a(4) = floor(4/3)*(4 - floor(4/3))*(4-floor(4/3)-1) = 1*3*2 = 6.

Maple

a:=n->floor(n/3)*(n-floor(n/3))*(n-floor(n/3)-1): seq(a(n), n=1..50);

Mathematica

A307559[n_] := #*(n - #)*(n - # - 1) & [Quotient[n, 3]];
Array[A307559, 50] (* Paolo Xausa, Jul 09 2026 *)

Crossrefs

Cf. A200067.

Sequence in context: A307252 A306625 A262986 * A211978 A028923 A187272

Adjacent sequences: A307556 A307557 A307558 * A307560 A307561 A307562

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 14 2019

Status

approved