A274208 Sum of the areas of all bargraphs of site-perimeter n.

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

Offset: 0

Author

Alois P. Heinz, Jun 13 2016

Keywords

• nonn

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

Crossrefs

Cf. A075126, A273347, A274207.

Formula

a(n) = Sum_{k=floor((n-1)/2)..floor(((n-1)^2+3)/12)} k * A274207(n,k).