A233506 Number of tilings of a 3 X 3 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

1, 14, 717, 62253, 4732061, 382882762, 31449389548, 2571574546111, 210607584419520, 17254476918858789, 1413637025226131703, 115812392270890399373, 9488271882367228634756, 777357166136453697810804, 63686950935296529029018801, 5217741644362129948411085318

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

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+3]=0, b(n, s(k=1, k+3=1, l)), 0)+
         `if`(k<=3 and l[k+3]=0 and l[k+6]=0,
            b(n, s(k=1, k+3=1, k+6=1, l)), 0)+
         `if`(irem(k, 3)>0 and l[k+1]=0,
            b(n, s(k=1, k+1=1, l)), 0)+
         `if`(irem(k, 3)=1 and l[k+1]=0 and l[k+2]=0,
            b(n, subsop(k=1, k+1=1, k+2=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$9]): s:=subsop:
seq(a(n), n=0..10);

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 <= 6 && l[[k+3]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1}]], 0] + If[k <= 3 && l[[k+3]] == 0 && l[[k+6]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1, k+6 -> 1}]], 0] + If[Mod[k, 3] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[Mod[k, 3] == 1 && 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&, 9]]; Table[a[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Dec 16 2013, translated from Maple *)

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233507, A233509.

Sequence in context: A223129 A303288 A277299 * A103426 A203750 A232158

Adjacent sequences: A233503 A233504 A233505 * A233507 A233508 A233509

Keyword

nonn

Author

Alois P. Heinz, Dec 11 2013

Status

approved