A233507 Number of tilings of a 2 X 4 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

1, 7, 201, 9787, 379688, 16512483, 726964790, 31549810845, 1378740599284, 60239603421159, 2630166605483293, 114886450998314920, 5017916294582867990, 219163121582772423673, 9572435654283943792842, 418094220600909382190818, 18261053013117932038592765

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Example

a(1) = A219866(4,2) = A129682(4) = A219866(2,4) = A219862(2) = 7:
._______. ._______. ._______. ._______.
|_____| | | |_____| | | | | | |___| | |
|_____|_| |_|_____| |_|_|_|_| |___|_|_|
._______. ._______. ._______.
| |___| | | | |___| |___|___|
|_|___|_| |_|_|___| |___|___|.

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<=6 and l[k+2]=0, b(n, s(k=1, k+2=1, l)), 0)+
         `if`(k<=4 and l[k+2]=0 and l[k+2*2]=0, b(n, s(k=1,
         k+2=1, k+2*2=1, l)), 0)+ `if`(irem(k, 2)>0 and
         l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$8]): s:= subsop:
seq(a(n), n=0..10);

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 <= 6 && l[[k + 2]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1}]], 0] + If[k <= 4 && l[[k+2]] == 0 && l[[k+2*2]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1, k+2*2 -> 1}]], 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&, 8]]; Table[Print[an = a[n]]; an, {n, 0, 16}] (* Jean-François Alcover, Dec 30 2013, translated from Maple *)

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233506, A233509.

Sequence in context: A221288 A355087 A276537 * A316862 A226414 A226345

Adjacent sequences: A233504 A233505 A233506 * A233508 A233509 A233510

Keyword

nonn

Author

Alois P. Heinz, Dec 11 2013

Status

approved