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.

1, 4, 45, 717, 9787, 148414, 2282036, 34688229, 530613082, 8119995275, 124183342755, 1899899589557, 29066650643742, 444678773140018, 6803102237763707, 104079849391557116, 1592303310404361651, 24360457647669398381, 372687643806340329749, 5701702230014416236396

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Example

a(1) = A219866(3,2) = A129682(3) = A219866(2,3) = A219867(2) = 4:
._____.  ._____.  ._____.  ._____.
|_____|  | | | |  |___| |  | |___|
|_____|  |_|_|_|  |___|_|  |_|___|.

Maple

s:= subsop:
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<=4 and l[k+2]=0,
         b(n, s(k=1, k+2=1, l))+ `if`(k<=2 and l[k+4]=0,
         b(n, s(k=1, k+2=1, k+4=1, l)), 0), 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$6]):
seq(a(n), n=0..25);

Mathematica

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 *)

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233505, A233506, A233507, A233509.

Sequence in context: A275125 A264123 A304645 * A126747 A107668 A214400

Adjacent sequences: A233310 A233311 A233312 * A233314 A233315 A233316

Keyword

nonn

Author

Alois P. Heinz, Dec 07 2013

Status

approved