BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-72-263
       ENTRY:: October 16, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: A procedure for improving the upper bound for the number of
               n-ominoes.
        TYPE:: Technical Report
      AUTHOR:: Klarner, David A.
      AUTHOR:: Rivest, Ronald L.
        DATE:: February 1972
       PAGES:: 36
    ABSTRACT:: An n-omino is a plane figure composed of n unit squares
               joined together along their edges. Every n-omino is generated
               by joining the edge of a unit square to the edge of a unit
               square in some (n-1)-omino so that the new square does not
               overlap any squares. Let t(n) denote the number of n-ominoes,
               then it is known that the sequence ${((t(n))}^{1/n} : n =
               1,2,\ldots )$ increases to a limit $\Theta$ , and 3.72 <
               $\Theta$ < 6.75 . A procedure exists for computing an
               increasing sequence of numbers bounded above by $\Theta$.
               (Chandra recently showed that the limit of this sequence is
               $\Theta$ .) In the present work we give a procedure for
               computing a sequence of numbers bounded below by $\Theta$ .
               Whether or not the limit of this sequence is $\Theta$ remains
               an open question. By computing the first ten terms of our
               sequence, we have shown that $\Theta$ < 4.65 .
       NOTES:: [Adminitrivia V1/Prg/19951016]
         END:: STAN//CS-TR-72-263