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Number of ways 5 domicules can be placed on an n X n square.
2

%I #9 Jun 05 2014 18:55:59

%S 0,0,0,0,33792,2307376,38049764,316687056,1756247962,7430841848,

%T 25895095920,77947547416,209206118486,511919916960,1160763672124,

%U 2468985096704,4973232330258,9557709330856,17631022607048,31372223986440,54066152166478,90552261553040

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

%H Alois P. Heinz, <a href="/A243467/b243467.txt">Table of n, a(n) for n = 0..1000</a>

%F 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.

%F 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.

%e a(4) = 33792:

%e +-------+ +-------+

%e |o-o o | | o o|

%e | \ | | / ||

%e | o o| |o o o o|

%e | \ | | X |

%e |o o o| | o o |

%e || / | | |

%e |o o | | o-o |

%e +-------+ +-------+ ... .

%p a:= n-> `if`(n<5, [0$4, 33792][n+1],((((((((((128*n-960)*n-1600)*n

%p +27360)*n-22560)*n-285192)*n+493090)*n+1279635)*n-2896628)

%p *n-2069823)*n+5464830)/15):

%p seq(a(n), n=0..30);

%Y Column k=5 of A243424.

%K nonn,easy

%O 0,5

%A _Alois P. Heinz_, Jun 05 2014