|
| |
|
|
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
|
|
|
|
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]];
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
