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A243465
Number of ways 3 domicules can be placed on an n X n square.
2
0, 0, 0, 180, 4890, 36028, 154434, 488660, 1271450, 2883900, 5907298, 11182644, 19877850, 33562620, 54291010, 84691668, 128065754, 188492540, 270942690, 381399220, 526986138, 716104764, 958577730, 1265800660, 1650901530, 2128907708, 2716920674, 3434298420
OFFSET
0,4
LINKS
FORMULA
G.f.: 2*x^3*(15*x^6-167*x^5+320*x^4+686*x^3-2789*x^2-1815*x-90)/(x-1)^7.
a(n) = (2574-2328*n-144*n^5-96*n^4+1188*n^3-854*n^2+32*n^6)/3 for n>=3, a(n) = 0 for n<3.
EXAMPLE
a(3) = 180:
+-----+ +-----+ +-----+ +-----+
|o-o | | o | | o | | o |
| | | \ | | / | | / |
|o-o | |o o o| |o o | |o o o|
| | || | | | / | | X |
| o-o| |o o | |o o-o| | o o|
+-----+ +-----+ +-----+ +-----+ ... .
MAPLE
a:= n-> `if`(n<3, 0, ((((((32*n-144)*n-96)*n+1188)*n-854)
*n-2328)*n+2574)/3):
seq(a(n), n=0..50);
CROSSREFS
Column k=3 of A243424.
Sequence in context: A008432 A289318 A250146 * A271673 A008378 A214818
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 05 2014
STATUS
approved