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A128422 Projective plane crossing number of K_{4,n}. 5
0, 0, 0, 2, 4, 6, 10, 14, 18, 24, 30, 36, 44, 52, 60, 70, 80, 90, 102, 114, 126, 140, 154, 168, 184, 200, 216, 234, 252, 270, 290, 310, 330, 352, 374, 396, 420, 444, 468, 494, 520, 546, 574, 602, 630, 660, 690, 720, 752, 784, 816, 850, 884, 918, 954, 990, 1026 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..57.

Eric Weisstein's World of Mathematics, Complete Bipartite Graph

Eric Weisstein's World of Mathematics, Projective Plane Crossing Number

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

FORMULA

a(n) = floor(n/3)*(2n-3(floor(n/3)+1)).

a(n) = ceiling(n^2/3) - n. - Charles R Greathouse IV, Jun 06 2013

G.f.: -2*x^4 / ((x-1)^3*(x^2+x+1)). - Colin Barker, Jun 06 2013

a(n) = floor((n - 1)(n - 2) / 3). - Christopher Hunt Gribble, Oct 13 2009

a(n) = 2*A001840(n-3). - R. J. Mathar, Jul 21 2015

MATHEMATICA

Table[Floor[((n - 2)^2 + (n - 2))/3], {n, 1, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)

Table[Ceiling[n^2/3] - n, {n, 20}] (* Eric W. Weisstein, Sep 07 2018 *)

Table[(3 n^2 - 9 n + 4 - 4 Cos[2 n Pi/3])/9, {n, 20}] (* Eric W. Weisstein, Sep 07 2018 *)

LinearRecurrence[{2, -1, 1, -2, 1}, {0, 0, 0, 2, 4, 6}, 20] (* Eric W. Weisstein, Sep 07 2018 *)

CoefficientList[Series[-2 x^3/((-1 + x)^3 (1 + x + x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 07 2018 *)

PROG

(PARI) a(n)=(n-1)*(n-2)\3 \\ Charles R Greathouse IV, Jun 06 2013

CROSSREFS

Cf. A001840.

Sequence in context: A303744 A059254 A024518 * A309882 A098380 A007782

Adjacent sequences:  A128419 A128420 A128421 * A128423 A128424 A128425

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 02 2007

STATUS

approved

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Last modified August 9 04:39 EDT 2020. Contains 336319 sequences. (Running on oeis4.)