A342385 Triangle T(n,k) read by rows (n >= 0, 0 <= k <= n): first column is A001477 and column k > 0 is k*A028310.

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 4, 3, 4, 5, 4, 6, 6, 4, 5, 6, 5, 8, 9, 8, 5, 6, 7, 6, 10, 12, 12, 10, 6, 7, 8, 7, 12, 15, 16, 15, 12, 7, 8, 9, 8, 14, 18, 20, 20, 18, 14, 8, 9, 10, 9, 16, 21, 24, 25, 24, 21, 16, 9, 10, 11, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 11

Offset

0,4

Comments

Row sums: A177787(n) with A177787(0) = 0.

First subtriangle: A003991(n+1).

Second subtriangle: A173395(n+1).

A000290(n) is a subsequence via (2*n+1)-th rows.

Links

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened)

Formula

From Paolo Xausa, Nov 15 2023: (Start)

T(n,0) = T(n,n) = n.

T(n,k) = k*(n-k), for 0 < k < n. (End)

Example

Triangle begins:
  n\k|  0   1   2   3   4   5   6   7   8   9 ...
  ---+-------------------------------------------
   0 |  0;
   1 |  1,  1;
   2 |  2,  1,  2;
   3 |  3,  2,  2,  3;
   4 |  4,  3,  4,  3,  4;
   5 |  5,  4,  6,  6,  4,  5;
   6 |  6,  5,  8,  9,  8,  5,  6;
   7 |  7,  6, 10, 12, 12, 10,  6,  7;
   8 |  8,  7, 12, 15, 16, 15, 12,  7,  8;
   9 |  9,  8, 14, 18, 20, 20, 18, 14,  8,  9;
  ...

Mathematica

With[{rowmax=10}, Table[If[0<k<n, k(n-k), n], {n, 0, rowmax}, {k, 0, n}]] (* Paolo Xausa, Nov 15 2023 *)

Crossrefs

Cf. A000290, A001477, A003991, A028310, A173395, A177787.

Sequence in context: A344835 A082860 A342859 * A367108 A283845 A365543

Adjacent sequences: A342382 A342383 A342384 * A342386 A342387 A342388

Keyword

nonn,tabl

Author

Paul Curtz, Mar 10 2021

Extensions

Name edited by Paolo Xausa, Nov 15 2023

Status

approved