A096154 Number of tilings of {1...n} by translation and reflection of a single set.

1, 2, 2, 4, 2, 8, 2, 13, 6, 20, 2, 56, 2, 68, 12, 160, 2, 299, 2, 584, 18, 1028, 2, 2338, 8, 4100, 38, 8456, 2, 16576, 2, 33469, 30, 65540

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}.

Links

Table of n, a(n) for n=1..34.

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

Cf. A096202, A096203.

Sequence in context: A067538 A305982 A304102 * A270365 A200147 A235063

Adjacent sequences: A096151 A096152 A096153 * A096155 A096156 A096157

Keyword

nonn

Author

Jon Wild, Jul 26 2004

Extensions

More terms from Don Reble, Jul 04 2004

Status

approved