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

Author

Alois P. Heinz, Jun 14 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.

Links

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

Crossrefs

Cf. A075126, A274207.

Formula

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