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A243646 Number of ways three L-tiles can be placed on an n X n square.

%I A243646 #7 Jun 08 2014 12:48:43
%S A243646 0,0,0,0,11,196,1195,4544,13215,32276,69671,137120,251139,434180,
%T A243646 715891,1134496,1738295,2587284,3754895,5329856,7418171,10145220,
%U A243646 13657979,18127360,23750671,30754196,39395895,49968224,62801075,78264836,96773571,118788320,144820519
%N A243646 Number of ways three L-tiles can be placed on an n X n square.
%H A243646 Alois P. Heinz, <a href="/A243646/b243646.txt">Table of n, a(n) for n = 0..1000</a>
%F A243646 G.f.: x^4*(x^5-27*x^4+90*x^3-54*x^2-119*x-11) / (x-1)^7.
%F A243646 a(n) = (n^6-6*n^5-6*n^4+88*n^3-73*n^2-310*n+426)/6 for n>=4, a(n) = 0 for n<4.
%e A243646 a(4) = 11:
%e A243646 ._______.  ._______.  ._______.  ._______.
%e A243646 | |_|_|_|  | |_|_|_|  | |_| |_|  | |_| |_|
%e A243646 |___|_|_|  |___| |_|  |___|___|  |___|___|
%e A243646 | |_| |_|  | |_|___|  | |_|_|_|  |_| |_|_|
%e A243646 |___|___|  |___|_|_|  |___|_|_|  |_|___|_|
%e A243646 ._______.  ._______.  ._______.  ._______.
%e A243646 | |_| |_|  |_|_| |_|  |_|_| |_|  |_| |_|_|
%e A243646 |___|___|  | |_|___|  |_|_|___|  |_|___|_|
%e A243646 |_|_| |_|  |___| |_|  | |_| |_|  | |_| |_|
%e A243646 |_|_|___|  |_|_|___|  |___|___|  |___|___|
%e A243646 ._______.  ._______.  ._______.
%e A243646 |_|_| |_|  | |_|_|_|  |_| |_|_|
%e A243646 |_| |___|  |___| |_|  | |___|_|
%e A243646 | |___|_|  |_| |___|  |___| |_|
%e A243646 |___|_|_|  |_|___|_|  |_|_|___| .
%p A243646 a:= n-> `if`(n<4, 0, ((((((n-6)*n-6)*n+88)*n-73)*n-310)*n+426)/6):
%p A243646 seq(a(n), n=0..50);
%Y A243646 Column k=3 of A243608.
%K A243646 nonn,easy
%O A243646 0,5
%A A243646 _Alois P. Heinz_, Jun 08 2014