A243466 Number of ways 4 domicules can be placed on an n X n square.

0, 0, 0, 58, 18343, 362643, 2911226, 14601844, 54738489, 168157793, 446728228, 1062085146, 2312934779, 4690690399, 8967633918, 16312226288, 28436620141, 47781858189, 77746670984, 122966217718, 189647543823, 285968959211, 422550971074, 613006835244

Offset

0,4

Links

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

Formula

G.f.: -x^3*(196*x^9 -1380*x^8 -1019*x^7 +21464*x^6 -32073*x^5 -77546*x^4 +302915*x^3 +199644*x^2 +17821*x +58) / (x-1)^9.

a(n) = (-104802 +61647*n +50017*n^2 -35304*n^3 -4984*n^4 +6480*n^5 -448*n^6 -384*n^7 +64*n^8)/6 for n>=4, a(3) = 58, a(n) = 0 for n<3.

Example

a(3) = 58:
+-----+  +-----+  +-----+  +-----+
|o-o o|  |o o  |  |o-o o|  |o-o  |
|   / |  | \ \ |  |    ||  |     |
|o o  |  |o o o|  |o   o|  |o o o|
||    |  ||    |  ||    |  ||  X |
|o o-o|  |o o-o|  |o o-o|  |o o o|
+-----+  +-----+  +-----+  +-----+  ... .

Maple

a:= n-> `if`(n<4, [0$3, 58][n+1], ((((((((64*n-384)*n-448)*n
        +6480)*n-4984)*n-35304)*n+50017)*n+61647)*n-104802)/6):
seq(a(n), n=0..50);

Crossrefs

Column k=4 of A243424.

Sequence in context: A308391 A128934 A173955 * A201988 A116103 A116115

Adjacent sequences: A243463 A243464 A243465 * A243467 A243468 A243469

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 05 2014

Status

approved