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%I #20 Nov 13 2014 21:40:42
%S 1,1,2,6,39,467,10290,431842,33702357,4933399675,1353257600290,
%T 694985665826606,668743276018647665,1205268925168096642391,
%U 4069023157203412697840109,25732126785058509461002703360,304814553338563601845965453449729
%N Number of ways to tile an n X n square with 1 X 1, 2 X 2 and 3 X 3 tiles.
%p b:= proc(n, l) option remember; local i, k, s, t;
%p if max(l[])>n then 0 elif n=0 then 1
%p elif min(l[])>0 then t:=min(l[]); b(n-t, map(h->h-t, l))
%p else for k do if l[k]=0 then break fi od; s:=0;
%p for i from k to min(k+2, nops(l)) while l[i]=0 do s:=s+
%p b(n, [l[j]$j=1..k-1, 1+i-k$j=k..i, l[j]$j=i+1..nops(l)])
%p od; s
%p fi
%p end:
%p a:= n-> b(n, [0$n]):
%p seq(a(n), n=0..10); # _Alois P. Heinz_, Feb 05 2013
%Y Cf. A045846, A063443.
%K nonn
%O 0,3
%A _Geoffrey H. Morley_, Feb 05 2013
%E a(7)-a(16) from _Alois P. Heinz_, Feb 05 2013
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