A166278 Square array A(n,k), n,k>=0, read by antidiagonals: A(n,k) is the total element sum of the k-fold f transform applied to the length n sequence of 1's. And f returns a sorted result after multiplying the elements in its input sequence with 1, 2, 3,... in descending size order.

0, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 4, 6, 4, 0, 1, 6, 10, 10, 5, 0, 1, 8, 19, 20, 15, 6, 0, 1, 12, 33, 46, 35, 21, 7, 0, 1, 16, 63, 100, 94, 56, 28, 8, 0, 1, 24, 111, 220, 242, 172, 84, 36, 9, 0, 1, 32, 201, 488, 633, 514, 290, 120, 45, 10, 0, 1, 48, 369, 1104, 1643, 1518, 984, 460, 165, 55, 11

Offset

0,6

Links

Alois P. Heinz, Antidiagonals n = 0..140, flattened

Example

A(3,4) = 33, because f([1,1,1]) = [1,2,3], (f^2)([1,1,1]) = [3,3,4], (f^3)([1,1,1]) = [4,6,9], (f^4)([1,1,1]) = [9,12,12], and 9+12+12 = 33.
Square array A(n,k) begins:
  0,  0,  0,  0,   0,   0, ...
  1,  1,  1,  1,   1,   1, ...
  2,  3,  4,  6,   8,  12, ...
  3,  6, 10, 19,  33,  63, ...
  4, 10, 20, 46, 100, 220, ...
  5, 15, 35, 94, 242, 633, ...

Maple

f:= l-> sort([seq(sort(l, `>`)[i]*i, i=1..nops(l))]):
A:= (n, k)-> add(i, i=(f@@k)([1$n])):
seq(seq(A(n, d-n), n=0..d), d=0..15);

Mathematica

f[L_List] := f[L] = Sort[Reverse[Sort[L]]*Range[Length[L]]];
A[0, _] = 0; A[n_, 0] := n; A[n_, k_] := Total[Nest[f, Range[n], k-1]];
Table[A[n, k-n], {k, 0, 15}, {n, 0, k}] // Flatten (* Jean-François Alcover, Jun 07 2016 *)

Crossrefs

Columns k=0-3 give: A001477, A000217, A000292, A070893.

Rows n=0-2 give: A000004, A000012, A029744(k+2).

Main diagonal gives A261490.

Sequence in context: A139600 A198321 A325003 * A365515 A316269 A242379

Adjacent sequences: A166275 A166276 A166277 * A166279 A166280 A166281

Keyword

easy,nonn,tabl

Author

Alois P. Heinz, Oct 10 2009

Status

approved