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 A214366 Number of different patterns using tiles from 1*1 to 1*n with each tile flush to at least one other. 2
 1, 1, 2, 65, 5562, 893395 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Flush means that two tiles have an edge in common. From Jon Perry, May 03 2013: (Start) If we require all tiles to be flush to each other, then the sequence is 1, 1, 2, 6, 0, 0, .... with a(n)=0 for n>=4. The 6 patterns for n=3 are: xxx   xxx   xxx   oxxx  +xxx   xxx oo+   o+     o+   o+    oo    oo+       o      o A proof for a(n)=0 for n>=4 is that these 6 patterns represent all possible 'hinge' patterns for any set of tiles, and by observation no 4th tile is admissible. (end) LINKS Giovanni Resta, Illustration of a(3) EXAMPLE For n=2 we have:      + +oo  oo For n=3 some examples are: +    o+    o    o oo   o     o    o+ xxx  xxx  xxx+  xxx To calculate a(3) we use the 9 basic patterns: o     o o     o   oo   oo    o xxx  xxx  xxx   xxx  oxxx  ooxxx 11   6    9    10    11    7 +     + xxx  xxx  +xxx 5    2    4 and calculate the number of valid positions for the 1*1 tile (top row) and for the 1*2 tile (bottom row). CROSSREFS Sequence in context: A198665 A185029 A228081 * A220596 A003821 A055765 Adjacent sequences:  A214363 A214364 A214365 * A214367 A214368 A214369 KEYWORD nonn,more AUTHOR Jon Perry, Feb 16 2013 EXTENSIONS a(4) from Giovanni Resta, Feb 21 2013 a(5) from Giovanni Resta, Mar 12 2013 STATUS approved

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Last modified October 16 21:57 EDT 2018. Contains 316275 sequences. (Running on oeis4.)