A342385 - OEIS

%I #17 Nov 22 2023 22:27:18

%S 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,

%T 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,

%U 24,25,24,21,16,9,10,11,10,18,24,28,30,30,28,24,18,10,11

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

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

%C First subtriangle: A003991(n+1).

%C Second subtriangle: A173395(n+1).

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

%H Paolo Xausa, <a href="/A342385/b342385.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of the triangle, flattened)

%F From _Paolo Xausa_, Nov 15 2023: (Start)

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

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

%e Triangle begins:

%e   n\k|  0   1   2   3   4   5   6   7   8   9 ...

%e   ---+-------------------------------------------

%e    0 |  0;

%e    1 |  1,  1;

%e    2 |  2,  1,  2;

%e    3 |  3,  2,  2,  3;

%e    4 |  4,  3,  4,  3,  4;

%e    5 |  5,  4,  6,  6,  4,  5;

%e    6 |  6,  5,  8,  9,  8,  5,  6;

%e    7 |  7,  6, 10, 12, 12, 10,  6,  7;

%e    8 |  8,  7, 12, 15, 16, 15, 12,  7,  8;

%e    9 |  9,  8, 14, 18, 20, 20, 18, 14,  8,  9;

%e   ...

%t With[{rowmax=10},Table[If[0<k<n,k(n-k),n],{n,0,rowmax},{k,0,n}]] (* _Paolo Xausa_, Nov 15 2023 *)

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

%K nonn,tabl

%O 0,4

%A _Paul Curtz_, Mar 10 2021

%E Name edited by _Paolo Xausa_, Nov 15 2023