A243465 Number of ways 3 domicules can be placed on an n X n square.

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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A243462 A243463 A243464 * A243466 A243467 A243468

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 05 2014

Status

approved