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A243646
Number of ways three L-tiles can be placed on an n X n square.
2
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
0,5
LINKS
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.
EXAMPLE
a(4) = 11:
._______. ._______. ._______. ._______.
| |_|_|_| | |_|_|_| | |_| |_| | |_| |_|
|___|_|_| |___| |_| |___|___| |___|___|
| |_| |_| | |_|___| | |_|_|_| |_| |_|_|
|___|___| |___|_|_| |___|_|_| |_|___|_|
._______. ._______. ._______. ._______.
| |_| |_| |_|_| |_| |_|_| |_| |_| |_|_|
|___|___| | |_|___| |_|_|___| |_|___|_|
|_|_| |_| |___| |_| | |_| |_| | |_| |_|
|_|_|___| |_|_|___| |___|___| |___|___|
._______. ._______. ._______.
|_|_| |_| | |_|_|_| |_| |_|_|
|_| |___| |___| |_| | |___|_|
| |___|_| |_| |___| |___| |_|
|___|_|_| |_|___|_| |_|_|___| .
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);
CROSSREFS
Column k=3 of A243608.
Sequence in context: A201185 A345342 A218818 * A186251 A234628 A105124
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 08 2014
STATUS
approved