A193470 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(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-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