A300474 Number of partitions of the square resulting from a sequence of n n-sections, each of which divides any part perpendicular to any of the axes.
1, 1, 8, 96, 2240, 80960, 4021248, 255704064, 19878918144, 1829788646400, 194788537180160, 23556611967336448, 3191162612827078656, 478807179615908462592, 78833945248222913495040, 14133035289273287214366720, 2740751307013005651817267200
Offset: 0
Keywords
Examples
a(2) = 8: ._______. ._______. ._______. ._______. | | | | | | | | |_______| | | | | | | | | | | |_______| |_______| | | | | | | | | | | |_______| |_|_|___| |___|_|_| |_______| |_______| ._______. ._______. ._______. ._______. | | | | | | | | | | | |___| | | |___| |___|___| |_______| | | | | | | | | | | | |___|___| |___|___| |_______| |___|___|. .
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..50
Programs
-
Maple
a:= proc(n) option remember; `if`(n<2, 1, coeff(series( RootOf(G-x-2*G^n+G^(n^2), G), x, n^2-n+2), x, n^2-n+1)) end: seq(a(n), n=0..16); -
Mathematica
a[0] = a[1] = 1; a[n_] := Module[{G}, G[] = 0; Do[G[x] = 2 G[x]^n - G[x]^n^2 + x + O[x]^(n^2 - n + 2) // Normal, {n^2 - n + 2}]; Coefficient[G[x], x, n^2 - n + 1]]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Dec 29 2018, after Alois P. Heinz *)