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A193470 Square array A(n,k) (n>=1, k>=0) read by antidiagonals: A(n,0) = 0 and A(n,k) is the least integer > A(n,k-1) that can be expressed as a triangular number divided by n.

%I A193470 #26 Nov 07 2016 05:08:12
%S A193470 0,0,1,0,3,3,0,1,5,6,0,7,2,14,10,0,2,9,5,18,15,0,1,3,30,7,33,21,0,3,6,
%T A193470 9,34,12,39,28,0,15,4,11,11,69,15,60,36,0,4,17,13,13,21,75,22,68,45,0,
%U A193470 1,5,62,15,20,24,124,26,95,55,0,5,12,17,66,30,35,38,132,35,105,66
%N A193470 Square array A(n,k) (n>=1, k>=0) read by antidiagonals: A(n,0) = 0 and A(n,k) is the least integer > A(n,k-1) that can be expressed as a triangular number divided by n.
%e A193470 n\k  0   1   2    3    4     5     6     7
%e A193470 ------------------------------------------
%e A193470 1 |  0   1   3    6   10    15    21    28    A000217
%e A193470 2 |  0   3   5   14   18    33    39    60    A074378
%e A193470 3 |  0   1   2    5    7    12    15    22    A001318
%e A193470 4 |  0   7   9   30   34    69    75   124    A154260
%e A193470 5 |  0   2   3    9   11    21    24    38    A057569
%e A193470 6 |  0   1   6   11   13    20    35    46    A154293
%e A193470 7 |  0   3   4   13   15    30    33    54    A057570
%e A193470 8 |  0  15  17   62   66   141   147   252    A157716
%p A193470 A193470_rect := proc(n,k) local j,i,L; L := NULL; j := 0; while nops([L]) < k do add(i/n, i=1..j); if type(%,integer) then L := L,% fi; j := j+1 od; L end:
%p A193470 seq(print(A193470_rect(n, 12)),n = 1..8);
%t A193470 a[_, 0] = 0; a[n_, k_] := a[n, k] = For[j = a[n, k-1]+1, True, j++, If[Reduce[m > 0 && j == m(m+1)/(2n), m, Integers] =!= False, Return[j]]]; Table[a[n-k, k], {n, 1, 12}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Nov 07 2016 *)
%Y A193470 Cf. A061782, A011772.
%K A193470 nonn,tabl
%O A193470 1,5
%A A193470 _Peter Luschny_, Jul 27 2011