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%I #14 Dec 16 2013 08:50:04
%S 1,14,717,62253,4732061,382882762,31449389548,2571574546111,
%T 210607584419520,17254476918858789,1413637025226131703,
%U 115812392270890399373,9488271882367228634756,777357166136453697810804,63686950935296529029018801,5217741644362129948411085318
%N Number of tilings of a 3 X 3 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.
%H Alois P. Heinz, <a href="/A233506/b233506.txt">Table of n, a(n) for n = 0..100</a>
%p b:= proc(n, l) option remember; local k, t; t:= min(l[]);
%p if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
%p else for k while l[k]>0 do od;
%p add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
%p `if`(k<=6 and l[k+3]=0, b(n, s(k=1, k+3=1, l)), 0)+
%p `if`(k<=3 and l[k+3]=0 and l[k+6]=0,
%p b(n, s(k=1, k+3=1, k+6=1, l)), 0)+
%p `if`(irem(k, 3)>0 and l[k+1]=0,
%p b(n, s(k=1, k+1=1, l)), 0)+
%p `if`(irem(k, 3)=1 and l[k+1]=0 and l[k+2]=0,
%p b(n, subsop(k=1, k+1=1, k+2=1, l)), 0)
%p fi
%p end:
%p a:=n-> b(n, [0$9]): s:=subsop:
%p seq(a(n), n=0..10);
%t b[n_, l_] := b[n, l] = Module[{k, t}, t := Min[l]; If [n == 0, 1, If[t > 0, b[n-t, l-t], k = 1; While[l[[k]] > 0, k++ ]; Sum[If[n >= j, b[n, ReplacePart[l, k -> j]], 0], {j, 2, 3}] + If[k <= 6 && l[[k+3]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1}]], 0] + If[k <= 3 && l[[k+3]] == 0 && l[[k+6]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1, k+6 -> 1}]], 0] + If[Mod[k, 3] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[Mod[k, 3] == 1 && l[[k+1]] == 0 && l[[k+2]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1, k+2 -> 1}]], 0] ]] ]; a[n_] := b[n, Array[0&, 9]]; Table[a[n], {n, 0, 10}] // Flatten (* _Jean-François Alcover_, Dec 16 2013, translated from Maple *)
%Y Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233507, A233509.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Dec 11 2013
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