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

%I A243649 #9 Jun 08 2014 12:47:23
%S A243649 0,0,0,0,0,2,3161,147502,2251309,19028431,111126797,503008566,
%T A243649 1888247929,6139119795,17805426945,47050056470,115056780421,
%U A243649 263499318031,570427305781,1175960541134,2322552621393,4416363482851,8118552261033,14478163221342,25121835774173
%N A243649 Number of ways six L-tiles can be placed on an n X n square.
%H A243649 Alois P. Heinz, <a href="/A243649/b243649.txt">Table of n, a(n) for n = 0..1000</a>
%F A243649 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.
%F A243649 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.
%e A243649 a(5) = 2:
%e A243649 ._________.   ._________.
%e A243649 | |_|_| |_|   |_| |_| |_|
%e A243649 |___| |___|   | |___|___|
%e A243649 |_| |___|_|   |___|_| |_|
%e A243649 | |___| |_|   | |_| |___|
%e A243649 |___|_|___|   |___|___|_| .
%p A243649 a:= n-> `if`(n<6, [0$5,2][n+1], ((((((((((((n-12)*n-39)*n+950)
%p A243649         *n-815)*n-29672)*n+69499)*n+452518)*n-1454446)*n
%p A243649         -3319216)*n+12944320)*n+9142512)*n-41687280)/720):
%p A243649 seq(a(n), n=0..40);
%Y A243649 Column k=6 of A243608.
%K A243649 nonn,easy
%O A243649 0,6
%A A243649 _Alois P. Heinz_, Jun 08 2014