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

%I A342385 #17 Nov 22 2023 22:27:18
%S A342385 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 A342385 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 A342385 24,25,24,21,16,9,10,11,10,18,24,28,30,30,28,24,18,10,11
%N A342385 Triangle T(n,k) read by rows (n >= 0, 0 <= k <= n): first column is A001477 and column k > 0 is k*A028310.
%C A342385 Row sums: A177787(n) with A177787(0) = 0.
%C A342385 First subtriangle: A003991(n+1).
%C A342385 Second subtriangle: A173395(n+1).
%C A342385 A000290(n) is a subsequence via (2*n+1)-th rows.
%H A342385 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 A342385 From _Paolo Xausa_, Nov 15 2023: (Start)
%F A342385 T(n,0) = T(n,n) = n.
%F A342385 T(n,k) = k*(n-k), for 0 < k < n. (End)
%e A342385 Triangle begins:
%e A342385   n\k|  0   1   2   3   4   5   6   7   8   9 ...
%e A342385   ---+-------------------------------------------
%e A342385    0 |  0;
%e A342385    1 |  1,  1;
%e A342385    2 |  2,  1,  2;
%e A342385    3 |  3,  2,  2,  3;
%e A342385    4 |  4,  3,  4,  3,  4;
%e A342385    5 |  5,  4,  6,  6,  4,  5;
%e A342385    6 |  6,  5,  8,  9,  8,  5,  6;
%e A342385    7 |  7,  6, 10, 12, 12, 10,  6,  7;
%e A342385    8 |  8,  7, 12, 15, 16, 15, 12,  7,  8;
%e A342385    9 |  9,  8, 14, 18, 20, 20, 18, 14,  8,  9;
%e A342385   ...
%t A342385 With[{rowmax=10},Table[If[0<k<n,k(n-k),n],{n,0,rowmax},{k,0,n}]] (* _Paolo Xausa_, Nov 15 2023 *)
%Y A342385 Cf. A000290, A001477, A003991, A028310, A173395, A177787.
%K A342385 nonn,tabl
%O A342385 0,4
%A A342385 _Paul Curtz_, Mar 10 2021
%E A342385 Name edited by _Paolo Xausa_, Nov 15 2023