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A200068 Irregular triangle read by rows: T(n,k), n>=0, 0<=k<=A200067(n), is number of compositions of n such that the sum of weighted inversions equals k and weights are products of absolute differences and distances between the element pairs which are not in sorted order. 2
1, 1, 2, 3, 1, 5, 1, 1, 1, 7, 3, 1, 3, 0, 0, 2, 11, 4, 2, 4, 3, 1, 3, 0, 1, 1, 1, 0, 1, 15, 8, 3, 8, 3, 3, 7, 1, 2, 3, 1, 3, 2, 0, 1, 2, 0, 0, 1, 0, 1, 22, 11, 7, 12, 4, 5, 13, 5, 4, 7, 4, 4, 5, 0, 3, 6, 2, 1, 2, 1, 2, 3, 0, 0, 2, 1, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Rows n = 0..28, flattened

EXAMPLE

The compositions of n = 4 have weighted inversions 0: [4], [2,2], [1,3], [1,1,2], [1,1,1,1]; 1: [1,2,1]; 2: [3,1]; 3: [2,1,1];  => row 4 = [5,1,1,1].

Irregular triangle begins:

   1;

   1;

   2;

   3, 1;

   5, 1, 1, 1;

   7, 3, 1, 3, 0, 0, 2;

  11, 4, 2, 4, 3, 1, 3, 0, 1, 1, 1, 0, 1;

  15, 8, 3, 8, 3, 3, 7, 1, 2, 3, 1, 3, 2, 0, 1, 2, 0, 0, 1, 0, 1;

  ...

MAPLE

T:= proc(n) option remember; local mx, b, p;

      b:=proc(m, i, l) local h;

           if m=0 then p(i):= p(i)+1; if i>mx then mx:=i fi

         else seq(b(m-h, i +add(`if`(l[j]<h, j*(h-l[j]), 0),

                  j=1..nops(l)), [h, l[]]), h=1..m) fi

         end;

      mx:=0;

      p:= proc() 0 end; forget(p);

      b(n, 0, []); seq(p(i), i=0..mx)

    end:

seq(T(n), n=0..10);

CROSSREFS

Cf. A000041 (column k=0), A024786(n-1) (column k=1), A011782 (row sums), A200067 (row lengths -1), A189074.

Sequence in context: A080063 A187680 A140706 * A139764 A227643 A249386

Adjacent sequences:  A200065 A200066 A200067 * A200069 A200070 A200071

KEYWORD

nonn,tabf,look

AUTHOR

Alois P. Heinz, Nov 13 2011

STATUS

approved

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Last modified August 22 06:01 EDT 2019. Contains 326172 sequences. (Running on oeis4.)