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A274217
Sum of the site-perimeters of all bargraphs of area n.
1
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
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
Sequence in context: A258457 A279152 A317780 * A162740 A324943 A301875
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 14 2016
STATUS
approved