

A127446


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


5



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
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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 !! (n1) !! (k1)
a127446_row n = a127446_tabl !! (n1)
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



