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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. 3
1, 1, 8, 96, 2240, 80960, 4021248, 255704064, 19878918144, 1829788646400, 194788537180160, 23556611967336448, 3191162612827078656, 478807179615908462592, 78833945248222913495040, 14133035289273287214366720, 2740751307013005651817267200 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Dec 29 2018, after Alois P. Heinz *)

CROSSREFS

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

Sequence in context: A224767 A337597 A052127 * A317005 A002506 A318012

Adjacent sequences:  A300471 A300472 A300473 * A300475 A300476 A300477

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 15 2018

STATUS

approved

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Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)