A274217 Sum of the site-perimeters of all bargraphs of area n.

0, 4, 12, 30, 72, 166, 376, 837, 1844, 4025, 8723, 18789, 40263, 85892, 182515, 386488, 815890, 1717604, 3606854, 7556995, 15800562, 32974263, 68694801, 142882147, 296749381, 615468930, 1274878193, 2637637046, 5451035408, 11253593442, 23210232132, 47826554753

Offset

0,2

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.

Links

Table of n, a(n) for n=0..31.

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>=4} k * A274207(k,n).

Crossrefs

Cf. A075126, A274207.

Sequence in context: A258457 A279152 A317780 * A162740 A324943 A301875

Adjacent sequences: A274214 A274215 A274216 * A274218 A274219 A274220

Keyword

nonn

Author

Alois P. Heinz, Jun 14 2016

Status

approved