A112986 Crossing number of K_{4,n} on the real projective plane.
0, 0, 0, 3, 5, 7, 18, 22, 26, 45, 51, 57, 84, 92, 100, 135, 145, 155, 198, 210, 222, 273, 287, 301, 360, 376, 392, 459, 477, 495, 570, 590, 610, 693, 715, 737, 828, 852, 876, 975, 1001, 1027, 1134, 1162, 1190, 1305, 1335, 1365, 1488, 1520, 1552, 1683, 1717, 1751, 1890
Offset: 0
Links
- Pak Tung Ho, The crossing number of K_{4,n} on the real projective plane, Discr. Math., 304 (2005), pp. 23-33.
- Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).
Crossrefs
Cf. A008724.
Programs
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Mathematica
a[n_] := Floor[n/3]*(2*n - 3); Array[a, 100, 0] (* Amiram Eldar, May 15 2024 *)
Formula
a(n) = floor(n/3)*(2*n-3). [Corrected by Amiram Eldar, May 15 2024]
G.f.: -x^3*(5*x^3+2*x^2+2*x+3) / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Mar 06 2014
Sum_{n>=3} 1/a(n) = 2*log(2)/3 + 6 - sqrt(3)*Pi. - Amiram Eldar, May 15 2024