A182568 a(n) = 2*floor(n/4)*(n - 2*(1 + floor(n/4))).

0, 0, 0, 0, 0, 2, 4, 6, 8, 12, 16, 20, 24, 30, 36, 42, 48, 56, 64, 72, 80, 90, 100, 110, 120, 132, 144, 156, 168, 182, 196, 210, 224, 240, 256, 272, 288, 306, 324, 342, 360, 380, 400, 420, 440, 462, 484, 506, 528, 552, 576, 600, 624, 650, 676, 702, 728, 756, 784, 812, 840, 870, 900, 930, 960, 992, 1024, 1056, 1088, 1122, 1156, 1190, 1224, 1260, 1296, 1332, 1368

Offset: 0

Author

N. J. A. Sloane, May 05 2012

Keywords

• nonn
• easy

Links

• Pak Tung Ho, The toroidal crossing number of K_{4,n}, Discrete Math. 309 (2009), no. 10, 3238--3248. MR2526742(2010i:05088).
• Eric Weisstein's World of Mathematics, Complete Bipartite Graph
• Eric Weisstein's World of Mathematics, Toroidal Crossing Number
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Crossrefs

Cf. A001972, A130519.

Programs

Mathematica

Table[2 Floor[n/4] (n - 2 (1 + Floor[n/4])), {n, 0, 20}] (* or *)
Table[(5 - (-1)^n + 2 (n - 4) n - 4 Cos[n Pi/2])/8, {n, 0, 20}] (* or *)
Table[(5 - (-1)^n - 2 (-I)^n - 2 I^n - 8 n + 2 n^2)/8, {n, 0, 20}] (* or *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 2}, 80] (* or *)
CoefficientList[Series[-2 x^5/((-1 + x)^3 (1 + x + x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 11 2018 *)

Formula

From R. J. Mathar, Jun 28 2012: (Start)

G.f. -2*x^5 / ( (x + 1)*(x^2 + 1)*(x - 1)^3 ).

a(n) = 2*A001972(n-5) = 2*A130519(n-1). (End)

a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6). - Eric W. Weisstein, Sep 11 2018