A394479 Number of tilings of an n X n square using 1 X 1 squares (monominoes) and stairs hexominoes.

1, 1, 1, 2, 5, 15, 84, 684, 7221, 121895, 3039701, 107360841, 5666410312, 441695641072, 50162944160810, 8387439464942548, 2064864748376205193, 745686410820671870950, 395666957431781807246192, 308649521313122750899881410, 353674652432800724298111984055, 595409917522562486496050260596601, 1472974193810774390034577961745197521, 5353962489774042038836766450068054443609

Offset

0,4

Comments

The stairs hexomino is a 3 X 3 square with an L tromino in the upper right corner removed and no rotations are allowed (see the examples).

Links

Table of n, a(n) for n=0..23.

Wikipedia, Hexomino

Wikipedia, Tromino

Example

a(4) = 5:
  ._______.  ._______.  ._______.  ._______.  ._______.
  |_|_|_|_|  | |_|_|_|  |_| |_|_|  |_|_|_|_|  |_|_|_|_|
  |_|_|_|_|  |   |_|_|  |_|   |_|  | |_|_|_|  |_| |_|_|
  |_|_|_|_|  |_____|_|  |_|_____|  |   |_|_|  |_|   |_|
  |_|_|_|_|  |_|_|_|_|  |_|_|_|_|  |_____|_|  |_|_____|  .

Maple

a:= proc(n) option remember; local b; b:=
      proc(n, l) option remember; local k;
        if n<2 then 1
      elif min(l[])>0 then b(n-1, map(h->h-1, l))
      else for k while l[k]>0 do od; b(n, subsop(k=1, l))+
           `if`(n>2 and k<nops(l)-1 and l[k+1]=0 and l[k+2]=0,
                b(n, subsop(k=3, k+1=2, k+2=1, l)), 0)
        fi
      end: forget(b); b(n, [0$n])
    end:
seq(a(n), n=0..16);

Crossrefs

Cf. A000930, A066864, A140304, A193147, A396311.

Sequence in context: A133645 A090130 A090140 * A032267 A191477 A196196

Adjacent sequences: A394474 A394475 A394478 * A394480 A394481 A394482

Keyword

nonn

Author

Alois P. Heinz, May 21 2026

Status

approved