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

%I A243465 #7 Jun 05 2014 18:47:24
%S A243465 0,0,0,180,4890,36028,154434,488660,1271450,2883900,5907298,11182644,
%T A243465 19877850,33562620,54291010,84691668,128065754,188492540,270942690,
%U A243465 381399220,526986138,716104764,958577730,1265800660,1650901530,2128907708,2716920674,3434298420
%N A243465 Number of ways 3 domicules can be placed on an n X n square.
%H A243465 Alois P. Heinz, <a href="/A243465/b243465.txt">Table of n, a(n) for n = 0..1000</a>
%F A243465 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.
%F A243465 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.
%e A243465 a(3) = 180:
%e A243465 +-----+  +-----+  +-----+  +-----+
%e A243465 |o-o  |  |  o  |  |  o  |  |  o  |
%e A243465 |     |  |   \ |  | /   |  | /   |
%e A243465 |o-o  |  |o o o|  |o o  |  |o o o|
%e A243465 |     |  || |  |  | /   |  |   X |
%e A243465 |  o-o|  |o o  |  |o o-o|  |  o o|
%e A243465 +-----+  +-----+  +-----+  +-----+  ... .
%p A243465 a:= n-> `if`(n<3, 0, ((((((32*n-144)*n-96)*n+1188)*n-854)
%p A243465          *n-2328)*n+2574)/3):
%p A243465 seq(a(n), n=0..50);
%Y A243465 Column k=3 of A243424.
%K A243465 nonn,easy
%O A243465 0,4
%A A243465 _Alois P. Heinz_, Jun 05 2014