A243647 Number of ways four L-tiles can be placed on an n X n square.

0, 0, 0, 0, 1, 176, 3145, 22969, 106819, 376796, 1101151, 2805825, 6438909, 13602304, 26866541, 50186401, 89436655, 153088924, 253052339, 405702361, 633123801, 964595760, 1438347889, 2103619049, 3023051131, 4275452476, 5958967015, 8194686929, 11130748309

Offset

0,6

Links

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

Formula

G.f.: -x^4*(9*x^8 -102*x^7 +253*x^6 +179*x^5 -1340*x^4 +916*x^3 +1597*x^2 +167*x+1) / (x-1)^9.

a(n) = (n^8 -8*n^7 -14*n^6 +244*n^5 -201*n^4 -2428*n^3 +4042*n^2 +7700*n -15576) / 24 for n>=4, a(n) = 0 for n<4.

Example

a(4) = 1:
._______.
| |_| |_|
|___|___|
| |_| |_|
|___|___| .

Maple

a:= n-> `if`(n<4, 0, ((((((((n-8)*n-14)*n+244)*n-201)*n
         -2428)*n+4042)*n+7700)*n-15576)/24):
seq(a(n), n=0..50);

Crossrefs

Column k=4 of A243608.

Sequence in context: A290703 A077742 A027483 * A220919 A221635 A223411

Adjacent sequences: A243644 A243645 A243646 * A243648 A243649 A243650

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 08 2014

Status

approved