A352243 -id:A352243 - cp's OEIS frontend

A352244 Positive integers that can be expressed in at least two ways as (x-y)*(x^3-y^3).

57456, 80752, 124852, 229957, 355072, 366471, 630667, 919296, 1193200, 1292032, 1316875, 1371136, 1823472, 1997632, 2036097, 2687607, 3679312, 4251871, 4653936, 5681152, 5821552, 5863536, 6540912, 8905456, 8984196, 10090672, 10113012, 10504375, 10532592, 10789632, 10921456, 14708736

Offset: 1

Michel Marcus, Mar 09 2022, after a suggestion from Vincent Thill

nonn

Integers that appears at least twice in the A352242 triangle.

			57456 is a term since it is A352242(17,5) as well as A352242(26,20).
A term (not necessarily the first) that occurs at least three times in A352242 is 1641000816 = A352242(221,65) = A352242(338,260) = A352242(1955,1943). - _Robert Israel_, May 17 2024

David A. Corneth, Table of n, a(n) for n = 1..12994 (terms <= 10^14)
David A. Corneth, PARI program

Cf. A352242, A352243.

row(n) = vector(n-1, k, (n-k)*(n^3-k^3));
lista(nn) = {my(list = List(), n=2); while (3*n*(n-1)+1 <= nn, my(rown = row(n)); for (k=1, #rown, if (rown[k] <= nn, listput(list, rown[k]))); n++;); listsort(list); my(res = List()); for (n=1, #list, if (#select(x->(x==list[n]), list) > 1, if (!vecsearch(Vec(res), list[n]), listput(res, list[n])));); Vec(res);}

PARI
```
\\ See PARI link
```

A352242 Regular triangle T(n,k) = (n-k)*(n^3-k^3) for n>=2 and 1 <= k <= n-1, read by rows.

Original entry on oeis.org

7, 52, 19, 189, 112, 37, 496, 351, 196, 61, 1075, 832, 567, 304, 91, 2052, 1675, 1264, 837, 436, 127, 3577, 3024, 2425, 1792, 1161, 592, 169, 5824, 5047, 4212, 3325, 2416, 1539, 772, 217, 8991, 7936, 6811, 5616, 4375, 3136, 1971, 976, 271, 13300, 11907, 10432, 8869, 7236, 5575, 3952, 2457, 1204, 331

Offset: 2

Michel Marcus, Mar 09 2022

			Triangle begins:
     7;
    52,   19;
   189,  112,   37;
   496,  351,  196,  61;
  1075,  832,  567, 304,  91;
  2052, 1675, 1264, 837, 436, 127;
  ...

Michael De Vlieger, Table of n, a(n) for n = 2..11176 (rows n = 2..150, flattened)

Cf. A003215 (right diagonal), A138849 (left border).
Cf. A352243, A352244.
Cf. A055461, A132111.

Table[(n - k) (n^3 - k^3), {n, 2, 11}, {k, n - 1}] // Flatten (* Michael De Vlieger, Mar 09 2022 *)

row(n) = vector(n-1, k, (n-k)*(n^3-k^3));

T(n,k) = A055461(n,k)*A132111(n,k). - R. J. Mathar, Feb 10 2025

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A352244 Positive integers that can be expressed in at least two ways as (x-y)*(x^3-y^3).

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A352242 Regular triangle T(n,k) = (n-k)*(n^3-k^3) for n>=2 and 1 <= k <= n-1, read by rows.

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