cp's OEIS Frontend

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

%I A096154 #6 Oct 19 2017 11:00:23
%S A096154 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,
%T A096154 4100,38,8456,2,16576,2,33469,30,65540
%N A096154 Number of tilings of {1...n} by translation and reflection of a single set.
%C A096154 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.
%C A096154 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}.
%F A096154 a(n)-4 often seems to be a power of 2. - _Don Reble_
%e A096154 a(8)=13 because the following are the 13 tilings of {1...8}:
%e A096154 {{1},{2},{3},{4},{5},{6},{7},{8}} tile: {1}
%e A096154 {{1,2},{3,4},{5,6},{7,8}} tile: {1,2}
%e A096154 {{1,3},{2,4},{5,7},{6,8}} tile: {1,3}
%e A096154 {{1,5},{2,6},{3,7},{4,8}} tile: {1,5}
%e A096154 {{1,2,3,4},{5,6,7,8}} tile: {1,2,3,4}
%e A096154 {{1,2,3,5},{4,6,7,8}} tile: {1,2,3,5}
%e A096154 {{1,5,6,7},{2,3,4,8}} tile: {1,2,3,7}
%e A096154 {{1,2,4,6},{3,5,7,8}} tile: {1,2,4,6}
%e A096154 {{1,4,6,7},{2,3,5,8}} tile: {1,2,4,7}
%e A096154 {{1,2,5,6},{3,4,7,8}} tile: {1,2,5,6}
%e A096154 {{1,3,4,7},{2,5,6,8}} tile: {1,3,4,7}
%e A096154 {{1,3,5,7},{2,4,6,8}} tile: {1,3,5,7}
%e A096154 {{1,2,3,4,5,6,7,8}} tile: {1,2,3,4,5,6,7,8}
%Y A096154 Cf. A096202, A096203.
%K A096154 nonn
%O A096154 1,2
%A A096154 _Jon Wild_, Jul 26 2004
%E A096154 More terms from _Don Reble_, Jul 04 2004