

A274208


Sum of the areas of all bargraphs of siteperimeter n.


2



0, 0, 0, 0, 1, 0, 4, 6, 14, 36, 77, 168, 395, 851, 1921, 4254, 9461, 20991, 46619, 103360, 229461, 508731, 1128706, 2503028, 5552197, 12313707, 27313442, 60581866, 134384684, 298097515, 661300177, 1467072716, 3254847737, 7221496901, 16023112774, 35553756328
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OFFSET

0,7


COMMENTS

A bargraph is a polyomino whose bottom is a segment of the nonnegative xaxis and whose upper part is a lattice path starting at (0,0) and ending with its first return to the xaxis using steps U=(0,1), D=(0,1) and H=(1,0), where UD and DU are not allowed.
The siteperimeter of a polyomino is the number of exterior cells having a common edge with at least one polyomino cell.
a(n)^(1/n) tends to 2.222118... .  Vaclav Kotesovec, Jun 26 2016


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..820
M. BousquetMÃ©lou and A. Rechnitzer, The siteperimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86112.
Wikipedia, Polyomino


FORMULA

a(n) = Sum_{k=floor((n1)/2)..floor(((n1)^2+3)/12)} k * A274207(n,k).


CROSSREFS

Cf. A075126, A273347, A274207.
Sequence in context: A319766 A108516 A219774 * A077068 A277059 A096003
Adjacent sequences: A274205 A274206 A274207 * A274209 A274210 A274211


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Jun 13 2016


STATUS

approved



