A243649 Number of ways six L-tiles can be placed on an n X n square.

0, 0, 0, 0, 0, 2, 3161, 147502, 2251309, 19028431, 111126797, 503008566, 1888247929, 6139119795, 17805426945, 47050056470, 115056780421, 263499318031, 570427305781, 1175960541134, 2322552621393, 4416363482851, 8118552261033, 14478163221342, 25121835774173

Offset

0,6

Links

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

Formula

G.f.: -x^5*(97*x^13 -844*x^12 +2143*x^11 -3665*x^10 +26943*x^9 -113864*x^8 +167176*x^7 +102604*x^6 -568735*x^5 +363954*x^4 +579769*x^3 +106565*x^2 +3135*x +2) / (x-1)^13.

a(n) = (n^12 -12*n^11 -39*n^10 +950*n^9 -815*n^8 -29672*n^7 +69499*n^6 +452518*n^5 -1454446*n^4 -3319216*n^3 +12944320*n^2 +9142512*n -41687280) / 720 for n>=6, a(5) = 2, a(n) = 0 for n<5.

Example

a(5) = 2:
._________.   ._________.
| |_|_| |_|   |_| |_| |_|
|___| |___|   | |___|___|
|_| |___|_|   |___|_| |_|
| |___| |_|   | |_| |___|
|___|_|___|   |___|___|_| .

Maple

a:= n-> `if`(n<6, [0$5, 2][n+1], ((((((((((((n-12)*n-39)*n+950)
        *n-815)*n-29672)*n+69499)*n+452518)*n-1454446)*n
        -3319216)*n+12944320)*n+9142512)*n-41687280)/720):
seq(a(n), n=0..40);

Crossrefs

Column k=6 of A243608.

Sequence in context: A158904 A358177 A175080 * A171154 A099689 A065671

Adjacent sequences: A243646 A243647 A243648 * A243650 A243651 A243652

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 08 2014

Status

approved