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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Example

a(2) = 8:
  ._______.  ._______.  ._______.  ._______.
  | | |   |  |   | | |  |_______|  |       |
  | | |   |  |   | | |  |_______|  |_______|
  | | |   |  |   | | |  |       |  |_______|
  |_|_|___|  |___|_|_|  |_______|  |_______|
  ._______.  ._______.  ._______.  ._______.
  |   |   |  |   |   |  |   |   |  |       |
  |___|   |  |   |___|  |___|___|  |_______|
  |   |   |  |   |   |  |       |  |   |   |
  |___|___|  |___|___|  |_______|  |___|___|.
  .

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 *)

Crossrefs

Cf. A091144, A236339, A237026, A300613, A322543.

Sequence in context: A360548 A337597 A052127 * A356590 A338571 A317005

Adjacent sequences: A300471 A300472 A300473 * A300475 A300476 A300477

Keyword

nonn

Author

Alois P. Heinz, Dec 15 2018

Status

approved