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A233509 Number of tilings of a 2 X 5 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

%I A233509 #13 Dec 31 2013 12:38:28
%S A233509 1,15,1062,148414,16512483,2043497465,257251613508,31941208907916,
%T A233509 3990164870713039,498504394558488109,62237975023439983192,
%U A233509 7773270324407375580946,970802515607358269506951,121240108673115249961266051,15141593230837339625055971170
%N A233509 Number of tilings of a 2 X 5 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.
%H A233509 Alois P. Heinz, <a href="/A233509/b233509.txt">Table of n, a(n) for n = 0..40</a>
%e A233509 a(1) = A219866(5,2) = A129682(5) = A219866(2,5) = A219868(2) = 15:
%e A233509 .___.  .___.  .___.  .___.  .___.  .___.  .___.  .___.
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%e A233509 |_|_|  |___|  |___|  |_|_|  |_|_|  |___|  |___|  |_|_|
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%e A233509 .___.  .___.  .___.  .___.  .___.  .___.  .___.
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%e A233509 |_|_|  |_|_|  |___|  |___|  |_| |  | |_|  | | |
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%e A233509 |_|_|  |___|  |_|_|  |___|  |_|_|  |_|_|  |___|.
%p A233509 b:= proc(n, l) option remember; local k, t; t:= min(l[]);
%p A233509       if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
%p A233509     else for k while l[k]>0 do od;
%p A233509          add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
%p A233509          `if`(k<=5 and l[k+5]=0, b(n, s(k=1, k+5=1, l)), 0)+
%p A233509          `if`(irem(k, 5)>0 and l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)+
%p A233509          `if`(irem(k, 5) in [$1..3] and l[k+1]=0 and l[k+2]=0,
%p A233509          b(n, s(k=1, k+1=1, k+2=1, l)), 0)
%p A233509       fi
%p A233509     end:
%p A233509 a:=n-> b(n, [0$10]): s:=subsop:
%p A233509 seq(a(n), n=0..4);
%t A233509 b[n_, l_] := b[n, l] = Module[{k, t}, t = Min[l]; Which[n == 0, 1, t > 0, b[n-t, l-t], True, For[k = 1, l[[k]] > 0, k++]; Sum[If[n >= j, b[n, ReplacePart[l, k -> j]], 0], {j, 2, 3}] + If[k <= 5 && l[[k+5]] == 0, b[n, ReplacePart[l, {k -> 1, k+5 -> 1}]], 0] + If[Mod[k, 5] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[1 <= Mod[k, 5] <= 3 && 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&, 10]]; Table[Print[an = a[n]]; an, {n, 0, 14}] (* _Jean-François Alcover_, Dec 30 2013, translated from Maple *)
%Y A233509 Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233506, A233507.
%K A233509 nonn
%O A233509 0,2
%A A233509 _Alois P. Heinz_, Dec 11 2013