A112986 - OEIS

%I #28 May 15 2024 01:30:51

%S 0,0,0,3,5,7,18,22,26,45,51,57,84,92,100,135,145,155,198,210,222,273,

%T 287,301,360,376,392,459,477,495,570,590,610,693,715,737,828,852,876,

%U 975,1001,1027,1134,1162,1190,1305,1335,1365,1488,1520,1552,1683,1717,1751,1890

%N Crossing number of K_{4,n} on the real projective plane.

%H Pak Tung Ho, <a href="http://dx.doi.org/10.1016/j.disc.2005.09.010">The crossing number of K_{4,n} on the real projective plane</a>, Discr. Math., 304 (2005), pp. 23-33.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).

%F a(n) = floor(n/3)*(2*n-3). [Corrected by _Amiram Eldar_, May 15 2024]

%F 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

%F Sum_{n>=3} 1/a(n) = 2*log(2)/3 + 6 - sqrt(3)*Pi. - _Amiram Eldar_, May 15 2024

%t a[n_] := Floor[n/3]*(2*n - 3); Array[a, 100, 0] (* _Amiram Eldar_, May 15 2024 *)

%Y Cf. A008724.

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_, Dec 24 2005