A179272 Sharp upper bound on Rosgen overlap number n-vertex graph with n >= 14, formula abused here for nonnegative integers.

-1, -2, -1, -1, 1, 2, 5, 7, 11, 14, 19, 23, 29, 34, 41, 47, 55, 62, 71, 79, 89, 98, 109, 119, 131, 142, 155, 167, 181, 194, 209, 223, 239, 254, 271, 287, 305, 322, 341, 359, 379, 398, 419, 439, 461, 482, 505, 527, 551, 574, 599, 623, 649, 674, 701, 727, 755, 782

Offset

0,2

Links

Table of n, a(n) for n=0..57.

Daniel W. Cranston, Nitish Korula, Timothy D. LeSaulnier, Kevin Milans, Christopher Stocker, Jennifer Vandenbussche, Douglas B. West, Overlap Number of Graphs, arXiv:1007.0804 [math.CO], Jul 06 2010.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). - R. J. Mathar, Jul 08 2010

Formula

a(n) = floor(n^2/4 - n/2 - 1).

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

a(n) = n - 1 + ceiling((1/4)*n^2), n>=1. - Clark Kimberling, Jan 07 2011

From Ilya Gutkovskiy, Jun 24 2016: (Start)

E.g.f.: (3*exp(-x) - (11 + 2*x - 2*x^2)*exp(x))/8.

a(n) = (2*n^2 - 4*n + 3*(-1)^n - 11)/8. (End)

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

Example

a(0) = floor(((0^2)/4) - (0/2) - 1) = floor(0 - 0 - 1) = -1.
a(1) = floor(((1^2)/4) - (1/2) - 1) = floor((1/4) - (1/2) - 1) = floor(-5/4) = -2.
a(2) = floor(((2^2)/4) - (2/2) - 1) = floor(1 - 1 - 1) = -1.
a(3) = floor(((3^2)/4) - (3/2) - 1) = floor(9/4 - 3/2 - 1) = floor(-1/4) = -1.
a(4) = floor(((4^2)/4) - (4/2) - 1) = floor(16/4 - 4/2 - 1) = floor(1) = 1.
a(5) = floor(((5^2)/4) - (5/2) - 1) = floor(16/4 - 5/2 - 1) = floor(11/4) = 2.
a(6) = floor(((6^2)/4) - (6/2) - 1) = floor(36/4 - 6/2 - 1) = floor(5) = 5.

Mathematica

Table[Ceiling[n/2] (2 + Ceiling[n/2] - Mod[n, 2]) - 1, {n, -3, 54}]; (* Fred Daniel Kline, Jun 24 2016 *)
CoefficientList[Series[(1 - 3 x^2 + x^3) / ((1 + x) (x - 1)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Nov 07 2016 *)

Crossrefs

Sequence in context: A336479 A221131 A126886 * A264753 A165680 A380162

Adjacent sequences: A179269 A179270 A179271 * A179273 A179274 A179275

Keyword

sign,easy

Author

Jonathan Vos Post, Jul 07 2010

Extensions

a(1) corrected by R. J. Mathar, Jul 08 2010

Status

approved