A185098 a(n) = floor((265/6)*4^(n-4) - n^2 - ((15+(-1)^(n-1))/6)* 2^(n-3)).

23, 141, 652, 2735, 11168, 44975, 180508, 722823, 2893168, 11575127, 46307132, 185237279, 740974336, 2963930847, 11855822524, 47423422103, 189694082672, 758776856135, 3035108998684, 12140438093295, 48561758666176, 194247043054991

Offset: 4

Author

Jonathan Vos Post, Mar 23 2011

Keywords

• nonn
• easy

Comments

An upper bound on the crossing number of the locally twisted n-dimensional hypercube LTQ(n). From Wang, p. 3. A lower bound is given in A188162 (may not be meaningful for n<4).

Examples

			a(4) = floor(((265 / 6) * (4^(4 - 4))) - ((4^2) + (((15 + ((-1)^(4 - 1))) / 6) * (2^(4 - 3))))) = floor(23.5) = 23.
a(5) = floor(((265 / 6) * (4^(5 - 4))) - ((5^2) + (((15 + ((-1)^(5 - 1))) / 6) * (2^(5 - 3))))) = floor(141) = 141.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..1000
• Haoli Wang, Xirong Xu, Yuansheng Yang, Bao Liu, Wenping Zheng and Guoqing Wang, The crossing number of locally twisted cubes, arXiv:1103.4227 [math.CO], Mar 22, 2011.

Crossrefs

Cf. A188162.

Programs

Magma

[Floor((265/6)*(4^(n-4))-(n^2 + ((15+(-1)^(n-1))/6)*(2^(n-3)))): n in [4..30]]; // Vincenzo Librandi, Mar 25 2012

Mathematica

Table[Floor[(265/6)*4^(n-4) - n^2 - ((15+(-1)^(n-1))/6)* 2^(n-3)], {n,4,50}] (* G. C. Greubel, Jun 22 2017 *)

PARI

a(n)=floor((265/6)*(4^(n-4))-(n^2 + ((15+(-1)^(n-1))/6)*(2^(n-3))))

Formula

Empirical G.f.: -x^4*(8*x^6-36*x^5+22*x^4+67*x^3-82*x^2-20*x+23) / ((x-1)^3*(2*x-1)*(2*x+1)*(4*x-1)). - Colin Barker, Dec 04 2012

Extensions

More terms from Franklin T. Adams-Watters, Mar 24 2011

More terms from Sean A. Irvine, May 24 2011