This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179272 #40 Oct 14 2024 08:11:11
%S A179272 -1,-2,-1,-1,1,2,5,7,11,14,19,23,29,34,41,47,55,62,71,79,89,98,109,
%T A179272 119,131,142,155,167,181,194,209,223,239,254,271,287,305,322,341,359,
%U A179272 379,398,419,439,461,482,505,527,551,574,599,623,649,674,701,727,755,782
%N A179272 Sharp upper bound on Rosgen overlap number n-vertex graph with n >= 14, formula abused here for nonnegative integers.
%H A179272 Daniel W. Cranston, Nitish Korula, Timothy D. LeSaulnier, Kevin Milans, Christopher Stocker, Jennifer Vandenbussche, Douglas B. West, <a href="http://arxiv.org/abs/1007.0804">Overlap Number of Graphs</a>, arXiv:1007.0804 [math.CO], Jul 06 2010.
%H A179272 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1). - _R. J. Mathar_, Jul 08 2010
%F A179272 a(n) = floor(n^2/4 - n/2 - 1).
%F A179272 a(n) = +2*a(n-1) -2*a(n-3) +a(n-4). G.f.: ( 1-3*x^2+x^3 ) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Jul 08 2010
%F A179272 a(n) = n - 1 + ceiling((1/4)*n^2), n>=1. - _Clark Kimberling_, Jan 07 2011
%F A179272 From _Ilya Gutkovskiy_, Jun 24 2016: (Start)
%F A179272 E.g.f.: (3*exp(-x) - (11 + 2*x - 2*x^2)*exp(x))/8.
%F A179272 a(n) = (2*n^2 - 4*n + 3*(-1)^n - 11)/8. (End)
%F A179272 b(n) = a(n-1) = floor ((n^2)/4 - 5/4) defines an even function for the sequence. - _Hartmut F. W. Hoft_, Nov 02 2016
%e A179272 a(0) = floor(((0^2)/4) - (0/2) - 1) = floor(0 - 0 - 1) = -1.
%e A179272 a(1) = floor(((1^2)/4) - (1/2) - 1) = floor((1/4) - (1/2) - 1) = floor(-5/4) = -2.
%e A179272 a(2) = floor(((2^2)/4) - (2/2) - 1) = floor(1 - 1 - 1) = -1.
%e A179272 a(3) = floor(((3^2)/4) - (3/2) - 1) = floor(9/4 - 3/2 - 1) = floor(-1/4) = -1.
%e A179272 a(4) = floor(((4^2)/4) - (4/2) - 1) = floor(16/4 - 4/2 - 1) = floor(1) = 1.
%e A179272 a(5) = floor(((5^2)/4) - (5/2) - 1) = floor(16/4 - 5/2 - 1) = floor(11/4) = 2.
%e A179272 a(6) = floor(((6^2)/4) - (6/2) - 1) = floor(36/4 - 6/2 - 1) = floor(5) = 5.
%t A179272 Table[Ceiling[n/2] (2 + Ceiling[n/2] - Mod[n, 2]) - 1, {n, -3, 54}]; (* _Fred Daniel Kline_, Jun 24 2016 *)
%t A179272 CoefficientList[Series[(1 - 3 x^2 + x^3) / ((1 + x) (x - 1)^3), {x, 0, 60}], x] (* _Vincenzo Librandi_, Nov 07 2016 *)
%K A179272 sign,easy
%O A179272 0,2
%A A179272 _Jonathan Vos Post_, Jul 07 2010
%E A179272 a(1) corrected by _R. J. Mathar_, Jul 08 2010