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.
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, 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, 1, 5, 62, 15, 20, 24, 124, 26, 95, 55, 0, 5, 12, 17, 66, 30, 35, 38, 132, 35, 105, 66
Offset: 1
Examples
n\k 0 1 2 3 4 5 6 7 ------------------------------------------ 1 | 0 1 3 6 10 15 21 28 A000217 2 | 0 3 5 14 18 33 39 60 A074378 3 | 0 1 2 5 7 12 15 22 A001318 4 | 0 7 9 30 34 69 75 124 A154260 5 | 0 2 3 9 11 21 24 38 A057569 6 | 0 1 6 11 13 20 35 46 A154293 7 | 0 3 4 13 15 30 33 54 A057570 8 | 0 15 17 62 66 141 147 252 A157716
Programs
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Maple
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: seq(print(A193470_rect(n, 12)),n = 1..8);
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Mathematica
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 *)