A374370 Square array read by antidiagonals: the n-th row lists n-gonal numbers that are products of smaller n-gonal numbers.

1, 4, 1, 6, 36, 1, 8, 45, 16, 1, 9, 210, 36, 10045, 1, 10, 300, 64, 11310, 2850, 1, 12, 378, 81, 20475, 61776, 6426, 1, 14, 630, 100, 52360, 79800, 9828, 1408, 1, 15, 780, 144, 197472, 103740, 35224, 61920, 265926, 1, 16, 990, 196, 230300, 145530, 60606, 67200, 391950, 69300, 1

Offset

2,2

Comments

If there are only finitely many solutions for a certain value of n, the rest of that row is filled with 0's.

The first term in each row is 1, because 1 is an n-gonal number for every n and it equals the empty product.

Links

Table of n, a(n) for n=2..56.

Example

Array begins:
   n=2: 1,      4,       6,       8,       9,       10,       12,       14
   n=3: 1,     36,      45,     210,     300,      378,      630,      780
   n=4: 1,     16,      36,      64,      81,      100,      144,      196
   n=5: 1,  10045,   11310,   20475,   52360,   197472,   230300,   341055
   n=6: 1,   2850,   61776,   79800,  103740,   145530,   437580,   719400
   n=7: 1,   6426,    9828,   35224,   60606,  1349460,  2077992,  3333330
   n=8: 1,   1408,   61920,   67200,  276640,   297045,   870485,  1022000
   n=9: 1, 265926,  391950, 1096200, 1767546,  1787500,  9909504, 28123200
  n=10: 1,  69300, 1297890, 4257000, 5756400,  9140040,  9729720, 10648800
  n=11: 1,  79135,  792330, 2382380, 5570565, 15361500, 22230000, 49888395
  n=12: 1,   9504,   45696,  604128, 1981980,  2208465,  4798080, 13837824

Crossrefs

Cf. A057145, A374371 (second column), A374498.

Rows: A018252 (n=2), A068143 (n=3 except first term), A062312 (n=4), A374372 (n=5), A374373 (n=6).

Sequence in context: A191714 A370356 A126150 * A364509 A349545 A291056

Adjacent sequences: A374367 A374368 A374369 * A374371 A374372 A374373

Keyword

nonn,tabl

Author

Pontus von Brömssen, Jul 07 2024

Status

approved