OFFSET
1,2
COMMENTS
a(n) counts the partitions of {1...n} with the property that all elements of the partition are congruent, modulo translation and reflection, to the same tile.
Two tilings that are reflections of each other are considered distinct. E.g. {{1,2,6},{3,7,8},{4,5,9}} and {{1,5,6},{2,3,7},{4,8,9}} are both included in the count for a(9). The first tile that allows more than one tiling for the same set without one being a reflection of the other is {1,2,7} on the span {1...12}.
FORMULA
a(n)-4 often seems to be a power of 2. - Don Reble
EXAMPLE
a(8)=13 because the following are the 13 tilings of {1...8}:
{{1},{2},{3},{4},{5},{6},{7},{8}} tile: {1}
{{1,2},{3,4},{5,6},{7,8}} tile: {1,2}
{{1,3},{2,4},{5,7},{6,8}} tile: {1,3}
{{1,5},{2,6},{3,7},{4,8}} tile: {1,5}
{{1,2,3,4},{5,6,7,8}} tile: {1,2,3,4}
{{1,2,3,5},{4,6,7,8}} tile: {1,2,3,5}
{{1,5,6,7},{2,3,4,8}} tile: {1,2,3,7}
{{1,2,4,6},{3,5,7,8}} tile: {1,2,4,6}
{{1,4,6,7},{2,3,5,8}} tile: {1,2,4,7}
{{1,2,5,6},{3,4,7,8}} tile: {1,2,5,6}
{{1,3,4,7},{2,5,6,8}} tile: {1,3,4,7}
{{1,3,5,7},{2,4,6,8}} tile: {1,3,5,7}
{{1,2,3,4,5,6,7,8}} tile: {1,2,3,4,5,6,7,8}
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Wild, Jul 26 2004
EXTENSIONS
More terms from Don Reble, Jul 04 2004
STATUS
approved