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%I #14 Feb 25 2019 08:24:06
%S 0,0,0,0,0,1,9,53,261,1165,4887,19642,76519,291095,1086946,3998430,
%T 14530223,52272218,186467253,660449671,2325124444,8143334776,
%U 28393762841,98621419068,341403900888,1178425064256,4057244213071,13937739553781,47786215201214,163554669548711
%N Sum of distances between leftmost and rightmost peaks in all bargraphs of semiperimeter n.
%H A. Blecher, C. Brennan, and A. Knopfmacher, <a href="http://dx.doi.org/10.1080/0035919X.2015.1059905">Peaks in bargraphs</a>, Trans. Royal Soc. South Africa, 71, No. 1, 2016, 97-103.
%F G.f.: -(4*x^6*(3-2*x^3+3*x^4 - sqx + x^2*(4-3*sqx) + 2*x*(sqx - 4))/((x^2-3*x+1)*sqx*(-1+2*x+x^2-sqx)^3)) where sqx = sqrt(x^4+2*x^2-4*x+1).
%e a(6)=1 since the bargraph with column heights 2,1,2 has a distance of 1 between first and last peak. All other bargraphs of semiperimeter 6 have at most one peak, hence 0 difference.
%o (PARI) my(x = 'x + O('x^30)); sqx = sqrt(x^4+2*x^2-4*x+1); concat(vector(5), Vec(-(4*x^6*(3-2*x^3+3*x^4 - sqx + x^2*(4-3*sqx) + 2*x*(sqx - 4))/((x^2-3*x+1)*sqx*(-1+2*x+x^2-sqx)^3)))) \\ _Michel Marcus_, Feb 25 2019
%Y Cf. A271941, A273720, A273345, A277973.
%K nonn
%O 1,7
%A _Arnold Knopfmacher_, Nov 08 2016