login
A342385
Triangle T(n,k) read by rows (n >= 0, 0 <= k <= n): first column is A001477 and column k > 0 is k*A028310.
1
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
KEYWORD
nonn,tabl
AUTHOR
Paul Curtz, Mar 10 2021
EXTENSIONS
Name edited by Paolo Xausa, Nov 15 2023
STATUS
approved