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A322495 Number of tilings of an n X n square using V (2m+1)-ominoes (m >= 0) in standard orientation. 1
1, 1, 2, 8, 68, 1262, 51420, 4577274, 888837716, 376116199534, 346688563051200, 695975307003529228 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The shapes of the tiles are:

                       ._.

              ._.      | |

       ._.    | |      | |

  ._.  | |_.  | |_._.  | |_._._.

  |_|  |___|  |_____|  |_______|  ... .

LINKS

Table of n, a(n) for n=0..11.

Wikipedia, Polyomino

EXAMPLE

a(3) = 8:

  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.

  |_|_|_|  | |_|_|  |_|_|_|  |_| |_|  |_|_|_|  |_| |_|  | |_|_|  | | |_|

  |_|_|_|  |___|_|  | |_|_|  |_|___|  |_| |_|  | |___|  | |_|_|  | |___|

  |_|_|_|  |_|_|_|  |___|_|  |_|_|_|  |_|___|  |___|_|  |_____|  |_____|.

.

MAPLE

b:= proc(n, l) option remember; local k, m, r;

      if n=0 or l=[] then 1

    elif min(l)>0 then (t-> b(n-t, map(h->h-t, l)))(min(l))

    elif l[-1]=n then b(n, subsop(-1=[][], l))

    else for k while l[k]>0 do od; r:= 0;

         for m from 0 while k+m<=nops(l) and l[k+m]=0 and n>m do

           r:= r+b(n, [l[1..k-1][], 1$m, m+1, l[k+m+1..nops(l)][]])

         od; r

      fi

    end:

a:= n-> b(n, [0$n]):

seq(a(n), n=0..9);

CROSSREFS

Main diagonal of A322494.

Sequence in context: A157752 A055547 A113087 * A332637 A239843 A099729

Adjacent sequences:  A322492 A322493 A322494 * A322496 A322497 A322498

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Dec 12 2018

STATUS

approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)