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%I #15 Feb 06 2017 12:39:25
%S 0,0,0,0,1,0,4,6,14,36,77,168,395,851,1921,4254,9461,20991,46619,
%T 103360,229461,508731,1128706,2503028,5552197,12313707,27313442,
%U 60581866,134384684,298097515,661300177,1467072716,3254847737,7221496901,16023112774,35553756328
%N Sum of the areas of all bargraphs of site-perimeter n.
%C A bargraph is a polyomino whose bottom is a segment of the nonnegative x-axis and whose upper part is a lattice path starting at (0,0) and ending with its first return to the x-axis using steps U=(0,1), D=(0,-1) and H=(1,0), where UD and DU are not allowed.
%C The site-perimeter of a polyomino is the number of exterior cells having a common edge with at least one polyomino cell.
%C a(n)^(1/n) tends to 2.222118... . - _Vaclav Kotesovec_, Jun 26 2016
%H Alois P. Heinz, <a href="/A274208/b274208.txt">Table of n, a(n) for n = 0..820</a>
%H M. Bousquet-Mélou and A. Rechnitzer, <a href="http://dx.doi.org/10.1016/S0196-8858(02)00553-5">The site-perimeter of bargraphs</a>, Adv. in Appl. Math. 31 (2003), 86-112.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%F a(n) = Sum_{k=floor((n-1)/2)..floor(((n-1)^2+3)/12)} k * A274207(n,k).
%Y Cf. A075126, A273347, A274207.
%K nonn
%O 0,7
%A _Alois P. Heinz_, Jun 13 2016
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