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A243465 Number of ways 3 domicules can be placed on an n X n square. 2

%I #7 Jun 05 2014 18:47:24

%S 0,0,0,180,4890,36028,154434,488660,1271450,2883900,5907298,11182644,

%T 19877850,33562620,54291010,84691668,128065754,188492540,270942690,

%U 381399220,526986138,716104764,958577730,1265800660,1650901530,2128907708,2716920674,3434298420

%N Number of ways 3 domicules can be placed on an n X n square.

%H Alois P. Heinz, <a href="/A243465/b243465.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 2*x^3*(15*x^6-167*x^5+320*x^4+686*x^3-2789*x^2-1815*x-90)/(x-1)^7.

%F a(n) = (2574-2328*n-144*n^5-96*n^4+1188*n^3-854*n^2+32*n^6)/3 for n>=3, a(n) = 0 for n<3.

%e a(3) = 180:

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

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

%e | | | \ | | / | | / |

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

%e | | || | | | / | | X |

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

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

%p a:= n-> `if`(n<3, 0, ((((((32*n-144)*n-96)*n+1188)*n-854)

%p *n-2328)*n+2574)/3):

%p seq(a(n), n=0..50);

%Y Column k=3 of A243424.

%K nonn,easy

%O 0,4

%A _Alois P. Heinz_, Jun 05 2014

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Last modified March 1 18:30 EST 2024. Contains 370443 sequences. (Running on oeis4.)