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A274208 Sum of the areas of all bargraphs of site-perimeter 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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.

The site-perimeter 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. Bousquet-Mélou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112.

Wikipedia, Polyomino

FORMULA

a(n) = Sum_{k=floor((n-1)/2)..floor(((n-1)^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

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)