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

0, 0, 0, 0, 11, 196, 1195, 4544, 13215, 32276, 69671, 137120, 251139, 434180, 715891, 1134496, 1738295, 2587284, 3754895, 5329856, 7418171, 10145220, 13657979, 18127360, 23750671, 30754196, 39395895, 49968224, 62801075, 78264836, 96773571, 118788320, 144820519

Offset: 0

Author

Alois P. Heinz, Jun 08 2014

Keywords

• nonn
• easy

Examples

			a(4) = 11:
._______.  ._______.  ._______.  ._______.
| |_|_|_|  | |_|_|_|  | |_| |_|  | |_| |_|
|___|_|_|  |___| |_|  |___|___|  |___|___|
| |_| |_|  | |_|___|  | |_|_|_|  |_| |_|_|
|___|___|  |___|_|_|  |___|_|_|  |_|___|_|
._______.  ._______.  ._______.  ._______.
| |_| |_|  |_|_| |_|  |_|_| |_|  |_| |_|_|
|___|___|  | |_|___|  |_|_|___|  |_|___|_|
|_|_| |_|  |___| |_|  | |_| |_|  | |_| |_|
|_|_|___|  |_|_|___|  |___|___|  |___|___|
._______.  ._______.  ._______.
|_|_| |_|  | |_|_|_|  |_| |_|_|
|_| |___|  |___| |_|  | |___|_|
| |___|_|  |_| |___|  |___| |_|
|___|_|_|  |_|___|_|  |_|_|___| .
		

Links

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

Crossrefs

Column k=3 of A243608.

Programs

Maple

a:= n-> `if`(n<4, 0, ((((((n-6)*n-6)*n+88)*n-73)*n-310)*n+426)/6):
seq(a(n), n=0..50);

Formula

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

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.