A188162 a(n) = ceiling( 4^n/20 - (n^2 + 1)*2^(n-1) ).

0, -1, -9, -36, -123, -364, -979, -2380, -5043, -7884, 717, 84788, 541901, 2659124, 11807949, 49984308, 206326989, 839988020, 3393375437, 13648999220, 54765341901, 219438854964, 878592183501, 3516214227764

Offset: 0

Author

Jonathan Vos Post, Mar 23 2011

Keywords

• sign
• easy

Comments

Lower bound on the crossing number of locally twisted n-dimensional hypercube LTQ(n). From Wang, p. 3.

Examples

			a(0) = ceiling(4^0 / 20) - ((0^2 + 1) * 2^(0 - 1)) = ceiling(-0.45) = 0.
a(1) = ceiling(4^1 / 20) - ((1^2 + 1) * 2^(1 - 1)) = ceiling(-1.8) = -1.
a(2) = ceiling(4^2 / 20) - ((2^2 + 1) * 2^(2 - 1)) = ceiling(-9.2) = -9.
a(3) = ceiling(4^3 / 20) - ((3^2 + 1) * 2^(3 - 1)) = ceiling(-36.8) = -36.
a(4) = ceiling(4^4 / 20) - ((4^2 + 1) * 2^(4 - 1)) = ceiling(-123.2) = -123.
		

Links

• Haoli Wang, Xirong Xu, Yuansheng Yang, Bao Liu, Wenping Zheng, Guoqing Wang, The crossing number of locally twisted cubes, arXiv:1103.4227 [math.CO], Mar 22, 2011.
• Index entries for linear recurrences with constant coefficients, signature (10,-35,46,4,-56,32)

Programs

Maple

A188162 := proc(n) 4^n/20 -(n^2+1)*2^(n-1) ; ceil(%) ; end proc:
seq(A188162(n),n=0..23) ; # R. J. Mathar, Mar 23 2011

Mathematica

Table[Ceiling[4^n/20-(n^2+1)2^(n-1)],{n,0,30}] (* or *) LinearRecurrence[ {10,-35,46,4,-56,32},{0,-1,-9,-36,-123,-364,-979},30] (* Harvey P. Dale, Dec 04 2020 *)

Formula

a(n) = 4^n/20 - (1+n^2)*2^(n-1) + 1/2 - 3*(-1)^n/10, n > 0. G.f.: x*(1 - x - 19*x^2 + 32*x^3 - 24*x^4 + 8*x^5) / ( (x-1)*(4*x-1)*(1+x)*(2*x-1)^3 ). - R. J. Mathar, Mar 24 2011