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A374370
Square array read by antidiagonals: the n-th row lists n-gonal numbers that are products of smaller n-gonal numbers.
5
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.
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
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved