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A300474
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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.
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3
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1, 1, 8, 96, 2240, 80960, 4021248, 255704064, 19878918144, 1829788646400, 194788537180160, 23556611967336448, 3191162612827078656, 478807179615908462592, 78833945248222913495040, 14133035289273287214366720, 2740751307013005651817267200
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listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..50
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EXAMPLE
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a(2) = 8:
._______. ._______. ._______. ._______.
| | | | | | | | |_______| | |
| | | | | | | | |_______| |_______|
| | | | | | | | | | |_______|
|_|_|___| |___|_|_| |_______| |_______|
._______. ._______. ._______. ._______.
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|___| | | |___| |___|___| |_______|
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|___|___| |___|___| |_______| |___|___|.
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A091144, A236339, A237026, A300613, A322543.
Sequence in context: A224767 A337597 A052127 * A338571 A317005 A002506
Adjacent sequences: A300471 A300472 A300473 * A300475 A300476 A300477
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Dec 15 2018
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STATUS
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approved
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