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 A096154 Number of tilings of {1...n} by translation and reflection of a single set. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)