A307559 - OEIS

%I #20 Jul 22 2022 08:01:49

%S 0,0,2,6,12,24,40,60,90,126,168,224,288,360,450,550,660,792,936,1092,

%T 1274,1470,1680,1920,2176,2448,2754,3078,3420,3800,4200,4620,5082,

%U 5566,6072,6624,7200,7800,8450,9126,9828,10584,11368,12180,13050,13950,14880,15872

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

%C 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).

%H M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, and I. Gutman, <a href="https://imi.pmf.kg.ac.rs/kjm/pub/13681216896539_tavakoligutman.pdf">Extremely irregular graphs</a>, Kragujevac J. Math., 37 (1), 2013, 135-139.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).

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

%F G.f.: 2*x^3*(1+x)*(1+x^2) / ( (1+x+x^2)^2*(x-1)^4 ). - _R. J. Mathar_, Jul 22 2022

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

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

%Y Cf. A200067.

%K nonn,easy

%O 1,3

%A _Emeric Deutsch_, Apr 14 2019