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%I #22 Dec 04 2020 18:52:38
%S 0,-1,-9,-36,-123,-364,-979,-2380,-5043,-7884,717,84788,541901,
%T 2659124,11807949,49984308,206326989,839988020,3393375437,13648999220,
%U 54765341901,219438854964,878592183501,3516214227764
%N a(n) = ceiling( 4^n/20 - (n^2 + 1)*2^(n-1) ).
%C Lower bound on the crossing number of locally twisted n-dimensional hypercube LTQ(n). From Wang, p. 3.
%H Haoli Wang, Xirong Xu, Yuansheng Yang, Bao Liu, Wenping Zheng, Guoqing Wang, <a href="http://arxiv.org/abs/1103.4227">The crossing number of locally twisted cubes</a>, arXiv:1103.4227 [math.CO], Mar 22, 2011.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,46,4,-56,32)
%F 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
%e a(0) = ceiling(4^0 / 20) - ((0^2 + 1) * 2^(0 - 1)) = ceiling(-0.45) = 0.
%e a(1) = ceiling(4^1 / 20) - ((1^2 + 1) * 2^(1 - 1)) = ceiling(-1.8) = -1.
%e a(2) = ceiling(4^2 / 20) - ((2^2 + 1) * 2^(2 - 1)) = ceiling(-9.2) = -9.
%e a(3) = ceiling(4^3 / 20) - ((3^2 + 1) * 2^(3 - 1)) = ceiling(-36.8) = -36.
%e a(4) = ceiling(4^4 / 20) - ((4^2 + 1) * 2^(4 - 1)) = ceiling(-123.2) = -123.
%p A188162 := proc(n) 4^n/20 -(n^2+1)*2^(n-1) ; ceil(%) ; end proc:
%p seq(A188162(n),n=0..23) ; # _R. J. Mathar_, Mar 23 2011
%t 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 *)
%K sign,easy
%O 0,3
%A _Jonathan Vos Post_, Mar 23 2011
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