OFFSET
0,2
LINKS
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
KEYWORD
sign,easy
AUTHOR
Jonathan Vos Post, Jul 07 2010
EXTENSIONS
a(1) corrected by R. J. Mathar, Jul 08 2010
STATUS
approved