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.

1, 15, 1062, 148414, 16512483, 2043497465, 257251613508, 31941208907916, 3990164870713039, 498504394558488109, 62237975023439983192, 7773270324407375580946, 970802515607358269506951, 121240108673115249961266051, 15141593230837339625055971170

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Example

a(1) = A219866(5,2) = A129682(5) = A219866(2,5) = A219868(2) = 15:
.___.  .___.  .___.  .___.  .___.  .___.  .___.  .___.
| | |  |___|  | | |  |___|  | | |  |___|  | | |  |___|
| | |  |___|  |_|_|  | | |  | | |  |___|  |_|_|  | | |
|_|_|  |___|  |___|  |_|_|  |_|_|  |___|  |___|  |_|_|
| | |  | | |  | | |  | | |  |___|  |___|  |___|  |___|
|_|_|  |_|_|  |_|_|  |_|_|  |___|  |___|  |___|  |___|
.___.  .___.  .___.  .___.  .___.  .___.  .___.
| | |  | | |  |___|  |___|  | | |  | | |  |___|
|_|_|  |_|_|  |___|  |___|  |_| |  | |_|  | | |
| | |  | | |  | | |  | | |  | |_|  |_| |  | | |
| | |  |_|_|  | | |  |_|_|  | | |  | | |  |_|_|
|_|_|  |___|  |_|_|  |___|  |_|_|  |_|_|  |___|.

Maple

b:= proc(n, l) option remember; local k, t; t:= min(l[]);
      if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
    else for k while l[k]>0 do od;
         add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
         `if`(k<=5 and l[k+5]=0, b(n, s(k=1, k+5=1, l)), 0)+
         `if`(irem(k, 5)>0 and l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)+
         `if`(irem(k, 5) in [$1..3] and l[k+1]=0 and l[k+2]=0,
         b(n, s(k=1, k+1=1, k+2=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$10]): s:=subsop:
seq(a(n), n=0..4);

Mathematica

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 *)

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233506, A233507.

Sequence in context: A241331 A205602 A370735 * A206162 A203409 A207980

Adjacent sequences: A233506 A233507 A233508 * A233510 A233511 A233512

Keyword

nonn

Author

Alois P. Heinz, Dec 11 2013

Status

approved