A243467 Number of ways 5 domicules can be placed on an n X n square.

0, 0, 0, 0, 33792, 2307376, 38049764, 316687056, 1756247962, 7430841848, 25895095920, 77947547416, 209206118486, 511919916960, 1160763672124, 2468985096704, 4973232330258, 9557709330856, 17631022607048, 31372223986440, 54066152166478, 90552261553040

Offset

0,5

Links

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

Formula

G.f.: 2*x^4*(465*x^11 -2767*x^10 -1161*x^9 -3873*x^8 +262965*x^7 -1067787*x^6 +1243269*x^5 +2069157*x^4 -9734826*x^3 -7263594*x^2 -967832*x -16896) / (x-1)^11.

a(n) = (5464830 -2069823*n -2896628*n^2 +1279635*n^3 +493090*n^4 -285192*n^5 -22560*n^6 +27360*n^7 -1600*n^8 -960*n^9 +128*n^10)/15 for n>=5, a(4) = 33792, a(n) = 0 for n<=3.

Example

a(4) = 33792:
+-------+  +-------+
|o-o o  |  |  o   o|
|     \ |  | /    ||
|  o   o|  |o o o o|
|   \   |  |   X   |
|o   o o|  |  o o  |
||    / |  |       |
|o   o  |  |  o-o  |
+-------+  +-------+   ... .

Maple

a:= n-> `if`(n<5, [0$4, 33792][n+1], ((((((((((128*n-960)*n-1600)*n
         +27360)*n-22560)*n-285192)*n+493090)*n+1279635)*n-2896628)
         *n-2069823)*n+5464830)/15):
seq(a(n), n=0..30);

Crossrefs

Column k=5 of A243424.

Sequence in context: A235516 A204949 A268909 * A205166 A238514 A252549

Adjacent sequences: A243464 A243465 A243466 * A243468 A243469 A243470

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 05 2014

Status

approved