A243646 - OEIS

%I #7 Jun 08 2014 12:48:43

%S 0,0,0,0,11,196,1195,4544,13215,32276,69671,137120,251139,434180,

%T 715891,1134496,1738295,2587284,3754895,5329856,7418171,10145220,

%U 13657979,18127360,23750671,30754196,39395895,49968224,62801075,78264836,96773571,118788320,144820519

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

%H Alois P. Heinz, <a href="/A243646/b243646.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x^4*(x^5-27*x^4+90*x^3-54*x^2-119*x-11) / (x-1)^7.

%F 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 a(4) = 11:

%e ._______.  ._______.  ._______.  ._______.

%e | |_|_|_|  | |_|_|_|  | |_| |_|  | |_| |_|

%e |___|_|_|  |___| |_|  |___|___|  |___|___|

%e | |_| |_|  | |_|___|  | |_|_|_|  |_| |_|_|

%e |___|___|  |___|_|_|  |___|_|_|  |_|___|_|

%e ._______.  ._______.  ._______.  ._______.

%e | |_| |_|  |_|_| |_|  |_|_| |_|  |_| |_|_|

%e |___|___|  | |_|___|  |_|_|___|  |_|___|_|

%e |_|_| |_|  |___| |_|  | |_| |_|  | |_| |_|

%e |_|_|___|  |_|_|___|  |___|___|  |___|___|

%e ._______.  ._______.  ._______.

%e |_|_| |_|  | |_|_|_|  |_| |_|_|

%e |_| |___|  |___| |_|  | |___|_|

%e | |___|_|  |_| |___|  |___| |_|

%e |___|_|_|  |_|___|_|  |_|_|___| .

%p a:= n-> `if`(n<4, 0, ((((((n-6)*n-6)*n+88)*n-73)*n-310)*n+426)/6):

%p seq(a(n), n=0..50);

%Y Column k=3 of A243608.

%K nonn,easy

%O 0,5

%A _Alois P. Heinz_, Jun 08 2014