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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 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.)