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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A277973 Sum of horizontal positions of the first peak in all bargraphs of semiperimeter n.

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%I A277973 #16 Jan 12 2024 17:25:35
%S A277973 0,0,0,1,6,25,91,311,1029,3346,10778,34544,110444,352785,1126885,
%T A277973 3601617,11521648,36899528,118322448,379908707,1221423149,3932113059,
%U A277973 12675055399,40909511880,132200481507,427718677728,1385419058692,4492446685542,14582927712740,47385785436719
%N A277973 Sum of horizontal positions of the first peak in all bargraphs of semiperimeter n.
%C A277973 Horizontal position is x-coordinate of the start of the leftmost horizontal step of the first peak.
%H A277973 Andrew Howroyd, <a href="/A277973/b277973.txt">Table of n, a(n) for n = 1..500</a>
%H A277973 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 A277973 G.f.: (2*x^3*(x^2-sqrt(x^4+2*x^2-4*x+1)+1)) / ((1-x)*(-x^2+sqrt(x^4+2*x^2-4*x+1)-2*x+1)^2).
%e A277973 For n = 4, a(4) = 1, as only the bargraph with first column of height one and second column of height two has horizontal position 1, all other cases are zero.
%o A277973 (PARI) seq(n) = my(r=sqrt((1 - x)*(1 - 3*x - x^2 - x^3) + O(x^(n-2)))); Vec(2*x^3*(1 + x^2 - r) / ((1 - x)*(1 - 2*x - x^2 + r)^2), -n) \\ _Andrew Howroyd_, Jan 12 2024
%Y A277973 Cf. A271941, A273720, A273345, A277999.
%K A277973 nonn
%O A277973 1,5
%A A277973 _Arnold Knopfmacher_, Nov 07 2016