A211348 Number of ways to tile an n X n square with 1 X 1, 2 X 2 and 3 X 3 tiles.

1, 1, 2, 6, 39, 467, 10290, 431842, 33702357, 4933399675, 1353257600290, 694985665826606, 668743276018647665, 1205268925168096642391, 4069023157203412697840109, 25732126785058509461002703360, 304814553338563601845965453449729

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Maple

b:= proc(n, l) option remember; local i, k, s, t;
      if max(l[])>n then 0 elif n=0 then 1
    elif min(l[])>0 then t:=min(l[]); b(n-t, map(h->h-t, l))
    else for k do if l[k]=0 then break fi od; s:=0;
         for i from k to min(k+2, nops(l)) while l[i]=0 do s:=s+
           b(n, [l[j]$j=1..k-1, 1+i-k$j=k..i, l[j]$j=i+1..nops(l)])
         od; s
      fi
    end:
a:= n-> b(n, [0$n]):
seq(a(n), n=0..10);  # Alois P. Heinz, Feb 05 2013

Mathematica

$RecursionLimit = 2048;
b[n_, l_] := b[n, l] = Module[{i, k, s, t}, Which[Max[l] > n, 0, n == 0, 1, Min[l] > 0, t = Min[l]; b[n - t, l - t], True, For[ k = 1, True, k++, If[l[[k]] == 0, Break[]]]; s = 0; For[i = k, i <= Min[k + 2, Length[l]] && l[[i]] == 0, i++, s += b[n, Join[l[[1 ;; k - 1]], Table[1 + i - k, {j, k, i}], l[[i + 1 ;; ]]]]]; s]];
a[n_] := b[n, Table[0, {n}]];
Table[Print[n]; a[n], {n, 0, 16}] (* Jean-François Alcover, Jan 31 2026,  after Alois P. Heinz *)

Crossrefs

Cf. A045846, A063443.

Sequence in context: A118324 A060421 A054970 * A295912 A120492 A028300

Adjacent sequences: A211345 A211346 A211347 * A211349 A211350 A211351

Keyword

nonn

Author

Geoffrey H. Morley, Feb 05 2013

Extensions

a(7)-a(16) from Alois P. Heinz, Feb 05 2013

Status

approved