cp's OEIS Frontend

A233313 Number of tilings of a 2 X 3 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

%I A233313 #16 Dec 16 2013 09:46:36
%S A233313 1,4,45,717,9787,148414,2282036,34688229,530613082,8119995275,
%T A233313 124183342755,1899899589557,29066650643742,444678773140018,
%U A233313 6803102237763707,104079849391557116,1592303310404361651,24360457647669398381,372687643806340329749,5701702230014416236396
%N A233313 Number of tilings of a 2 X 3 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.
%H A233313 Alois P. Heinz, <a href="/A233313/b233313.txt">Table of n, a(n) for n = 0..500</a>
%e A233313 a(1) = A219866(3,2) = A129682(3) = A219866(2,3) = A219867(2) = 4:
%e A233313 ._____.  ._____.  ._____.  ._____.
%e A233313 |_____|  | | | |  |___| |  | |___|
%e A233313 |_____|  |_|_|_|  |___|_|  |_|___|.
%p A233313 s:= subsop:
%p A233313 b:= proc(n, l) option remember; local k, t; t:= min(l[]);
%p A233313       if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
%p A233313     else for k while l[k]>0 do od; add(`if`(n>=j,
%p A233313          b(n, s(k=j, l)), 0), j=2..3)+ `if`(k<=4 and l[k+2]=0,
%p A233313          b(n, s(k=1, k+2=1, l))+ `if`(k<=2 and l[k+4]=0,
%p A233313          b(n, s(k=1, k+2=1, k+4=1, l)), 0), 0)+ `if`(
%p A233313          irem(k, 2)>0 and l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)
%p A233313       fi
%p A233313     end:
%p A233313 a:=n-> b(n, [0$6]):
%p A233313 seq(a(n), n=0..25);
%t A233313 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 <= 4 && l[[k+2]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1}]] + If[k <= 2 && l[[k+4]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1, k+4 -> 1}]], 0], 0] + If[Mod[k, 2] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] ] ] ]; a[n_] := b[n, Array[0&, 6]]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Dec 16 2013, translated from Maple *)
%Y A233313 Cf. A000931, A129682, A219866, A219867, A233505, A233506, A233507, A233509.
%K A233313 nonn
%O A233313 0,2
%A A233313 _Alois P. Heinz_, Dec 07 2013