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 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. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified May 21 04:17 EDT 2024. Contains 372720 sequences. (Running on oeis4.)