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

Author

N. J. A. Sloane, Dec 24 2005

Keywords

• nonn
• easy

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

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