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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
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 15 2018
STATUS
approved