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A243466 Number of ways 4 domicules can be placed on an n X n square.

%I A243466 #6 Jun 05 2014 18:48:56
%S A243466 0,0,0,58,18343,362643,2911226,14601844,54738489,168157793,446728228,
%T A243466 1062085146,2312934779,4690690399,8967633918,16312226288,28436620141,
%U A243466 47781858189,77746670984,122966217718,189647543823,285968959211,422550971074,613006835244
%N A243466 Number of ways 4 domicules can be placed on an n X n square.
%H A243466 Alois P. Heinz, <a href="/A243466/b243466.txt">Table of n, a(n) for n = 0..1000</a>
%F A243466 G.f.: -x^3*(196*x^9 -1380*x^8 -1019*x^7 +21464*x^6 -32073*x^5 -77546*x^4 +302915*x^3 +199644*x^2 +17821*x +58) / (x-1)^9.
%F A243466 a(n) = (-104802 +61647*n +50017*n^2 -35304*n^3 -4984*n^4 +6480*n^5 -448*n^6 -384*n^7 +64*n^8)/6 for n>=4, a(3) = 58, a(n) = 0 for n<3.
%e A243466 a(3) = 58:
%e A243466 +-----+  +-----+  +-----+  +-----+
%e A243466 |o-o o|  |o o  |  |o-o o|  |o-o  |
%e A243466 |   / |  | \ \ |  |    ||  |     |
%e A243466 |o o  |  |o o o|  |o   o|  |o o o|
%e A243466 ||    |  ||    |  ||    |  ||  X |
%e A243466 |o o-o|  |o o-o|  |o o-o|  |o o o|
%e A243466 +-----+  +-----+  +-----+  +-----+  ... .
%p A243466 a:= n-> `if`(n<4, [0$3, 58][n+1], ((((((((64*n-384)*n-448)*n
%p A243466         +6480)*n-4984)*n-35304)*n+50017)*n+61647)*n-104802)/6):
%p A243466 seq(a(n), n=0..50);
%Y A243466 Column k=4 of A243424.
%K A243466 nonn,easy
%O A243466 0,4
%A A243466 _Alois P. Heinz_, Jun 05 2014