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

0,7

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: A373567 A108516 A219774 * A077068 A277059 A096003

Adjacent sequences: A274205 A274206 A274207 * A274209 A274210 A274211

Keyword

nonn

Author

Alois P. Heinz, Jun 13 2016

Status

approved