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 A187816 Triangle read by rows in which row n lists the first 2^(n-1) terms of A006519 in nonincreasing order, n >= 1. 6
 1, 2, 1, 4, 2, 1, 1, 8, 4, 2, 2, 1, 1, 1, 1, 16, 8, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 32, 16, 8, 8, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 64, 32, 16, 16, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) is also the number of parts in the k-th largest region of the diagram of regions of the set of compositions of n, n >= 1, k >= 1, see example. Row lengths is A000079. Row sums give A001792(n-1). LINKS EXAMPLE For n = 5 the diagram of regions of the set of compositions of 5 has 2^(5-1) regions, see below: ------------------------------------------------------ .          A006519 .         as a tree .         of number        Diagram Region    of parts       of regions     Composition ------------------------------------------------------ .                         _ _ _ _ _ 1      | 1          |    |_| | | | |    1, 1, 1, 1, 1 2      |   2        |    |_ _| | | |    2, 1, 1, 1 3      | 1          |    |_|   | | |    1, 2, 1, 1 4      |      4     |    |_ _ _| | |    3, 1, 1 5      | 1          |    |_| |   | |    1, 1, 2, 1 6      |   2        |    |_ _|   | |    2, 2, 1 7      | 1          |    |_|     | |    1, 3, 1 8      |        8   |    |_ _ _ _| |    4, 1 9      | 1          |    |_| | |   |    1, 1, 1, 2 10     |   2        |    |_ _| |   |    2, 1, 2 11     | 1          |    |_|   |   |    1, 2, 2 12     |      4     |    |_ _ _|   |    3, 2 13     | 1          |    |_| |     |    1, 1, 3 14     |   2        |    |_ _|     |    2, 3 15     | 1          |    |_|       |    1, 4 16     |         16 |    |_ _ _ _ _|    5 . The first largest region in the diagram is the 16th region which contains 16 parts, so T(5,1) = 16. The second largest region is the 8th region which contains 8 parts, so T(5,2) = 8. The third and the fourth largest regions are both the 4th region and the 12th region, each contains 4 parts, so T(5,3) = 4 and T(5,4) = 4. And so on. The sequence of the number of parts of the k-th largest region of the diagram is [16, 8, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], the same as the 5th row of triangle, as shown below. Triangle begins: 1; 2,1; 4,2,1,1; 8,4,2,2,1,1,1,1; 16,8,4,4,2,2,2,2,1,1,1,1,1,1,1,1; 32,16,8,8,4,4,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1; ... CROSSREFS Cf. A000079, A001511, A001792, A006519, A011782, A065120, A187818, A228525, A228369. Sequence in context: A290935 A031424 A013942 * A088423 A006839 A268267 Adjacent sequences:  A187813 A187814 A187815 * A187817 A187818 A187819 KEYWORD nonn,tabf,easy AUTHOR Omar E. Pol, Sep 10 2013 STATUS approved

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Last modified June 16 13:05 EDT 2021. Contains 345057 sequences. (Running on oeis4.)