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

0,4

Links

Table of n, a(n) for n=0..54.

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).

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

Mathematica

a[n_] := Floor[n/3]*(2*n - 3); Array[a, 100, 0] (* Amiram Eldar, May 15 2024 *)

Crossrefs

Cf. A008724.

Sequence in context: A247164 A064080 A184875 * A052333 A074106 A002261

Adjacent sequences: A112983 A112984 A112985 * A112987 A112988 A112989

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 24 2005

Status

approved