%I #16 Jan 12 2024 17:25:35

%S 0,0,0,1,6,25,91,311,1029,3346,10778,34544,110444,352785,1126885,

%T 3601617,11521648,36899528,118322448,379908707,1221423149,3932113059,

%U 12675055399,40909511880,132200481507,427718677728,1385419058692,4492446685542,14582927712740,47385785436719

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

%C Horizontal position is x-coordinate of the start of the leftmost horizontal step of the first peak.

%H Andrew Howroyd, <a href="/A277973/b277973.txt">Table of n, a(n) for n = 1..500</a>

%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.: (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 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 (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 Cf. A271941, A273720, A273345, A277999.

%K nonn

%O 1,5

%A _Arnold Knopfmacher_, Nov 07 2016