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 A189074 Irregular triangle read by rows: T(n,k) = number of compositions of n with k inversions (n >= 0, 0 <= k <= floor(n^2/8). 2
 1, 1, 2, 3, 1, 5, 2, 1, 7, 5, 3, 1, 11, 8, 7, 4, 2, 15, 15, 14, 10, 6, 3, 1, 22, 23, 26, 21, 17, 10, 6, 2, 1, 30, 37, 44, 42, 36, 27, 19, 11, 6, 3, 1, 42, 55, 73, 74, 73, 60, 50, 34, 24, 13, 8, 4, 2, 56, 83, 115, 128, 133, 123, 109, 87, 68, 48, 32, 20, 12, 6, 3, 1, 77, 118, 177, 209, 235, 230, 223, 192, 166, 129, 100, 70, 51, 31, 20, 11, 6, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are powers of 2. The Heubach et. al. reference has a table for n <= 12. LINKS Alois P. Heinz, Rows n = 0..25, flattened S. Heubach, A. Knopfmacher, M. E. Mays and A. Munagi, Inversions in Compositions of Integers, to appear in Quaestiones Mathematicae. EXAMPLE T(4,0) = 5: [4], [1,3], [2,2], [1,1,2], [1,1,1,1] - all partitions of 4. T(5,2) = 3: [2,2,1], [3,1,1], [1,2,1,1]. T(6,4) = 2: [2,2,1,1], [2,1,1,1,1]. Triangle begins: 1 1 2 3   1 5   2  1 7   5  3  1 11  8  7  4  2 15 15 14 10  6  3 1 22 23 26 21 17 10 6 2 1 ... MAPLE T:= proc(n) option remember; local b, p;       b:=proc(m, i, l)            if m=0 then p(i):= p(i)+1          else seq (b(m-h, i+nops (select (j->j0). Lengths of rows are given by 1+A001972(n-3).  Row sums are A011782. Sequence in context: A214055 A066909 A095195 * A169615 A076791 A075014 Adjacent sequences:  A189071 A189072 A189073 * A189075 A189076 A189077 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Apr 16 2011 STATUS approved

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Last modified June 17 23:56 EDT 2013. Contains 226327 sequences.