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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

Table of n, a(n) for n=0..5.

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.)