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

1,5

Links

Table of n, a(n) for n=1..78.

Example

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

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);

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 *)

Crossrefs

Cf. A061782, A011772.

Sequence in context: A172169 A306629 A185282 * A102752 A104548 A085707

Adjacent sequences: A193467 A193468 A193469 * A193471 A193472 A193473

Keyword

nonn,tabl

Author

Peter Luschny, Jul 27 2011

Status

approved