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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 20 14:50 EDT 2019. Contains 326152 sequences. (Running on oeis4.)