A127446 Triangle T(n,k) = n*A051731(n,k) read by rows.

1, 2, 2, 3, 0, 3, 4, 4, 0, 4, 5, 0, 0, 0, 5, 6, 6, 6, 0, 0, 6, 7, 0, 0, 0, 0, 0, 7, 8, 8, 0, 8, 0, 0, 0, 8, 9, 0, 9, 0, 0, 0, 0, 0, 9, 10, 10, 0, 0, 10, 0, 0, 0, 0, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 12, 12, 12, 0, 12, 0, 0, 0, 0, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 14, 14, 0, 0, 0, 0, 14

Offset

1,2

Comments

Replace the 1's in row n of A051731 with n's.

T(n,k) is the sum of the k's in the partitions of n into equal parts. - Omar E. Pol, Nov 25 2019

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Formula

T(n,k) = k*A126988(n,k). - Omar E. Pol, Nov 25 2019

Example

First few rows of the triangle:
  1;
  2, 2;
  3, 0, 3;
  4, 4, 0, 4;
  5, 0, 0, 0, 5;
  6, 6, 6, 0, 0, 6;
  7, 0, 0, 0, 0, 0, 7;
  ...
For n = 6 the partitions of 6 into equal parts are [6], [3,3], [2,2,2], [1,1,1,1,1,1], so the sum of the k's are [6, 6, 6, 0, 0, 6] respectively, equaling the 6th row of triangle. - Omar E. Pol, Nov 25 2019

Maple

A127446 := proc(n, k) if n mod k = 0 then n; else 0; fi; end: for n from 1 to 20 do for k from 1 to n do printf("%d, ", A127446(n, k)) ; od: od: # R. J. Mathar, May 08 2009

Mathematica

Flatten[Table[If[Mod[n, k] == 0, n, 0], {n, 20}, {k, n}]] (* Vincenzo Librandi, Nov 02 2016 *)

Prog

(Haskell)
a127446 n k = a127446_tabl !! (n-1) !! (k-1)
a127446_row n = a127446_tabl !! (n-1)
a127446_tabl = zipWith (\v ws -> map (* v) ws) [1..] a051731_tabl
-- Reinhard Zumkeller, Jan 21 2014

Crossrefs

Cf. A038040 (row sums), A051731, A126988, A244051, A328362.

Sequence in context: A319929 A129234 A213081 * A046157 A035167 A071448

Adjacent sequences: A127443 A127444 A127445 * A127447 A127448 A127449

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jan 14 2007

Extensions

Edited and extended by R. J. Mathar, May 08 2009

Status

approved