A350210 -id:A350210 - cp's OEIS frontend

A350397 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if no such number exists.

305, 1980, 1900, 3321, 5256, 8310, 12516, 17108, 24832, 34249, 42381, 61697, 78766, 106956, 132994, 170325, 203415, 266595, 322943, 393828, 475520, 569416, 695799, 823447, 958300, 1149125, 1313545, 1565055, 1802736, 2088119, 2376250, 2748270, 3135195, 3548876

Offset: 3

Ilya Gutkovskiy, Dec 29 2021

nonn

			For n = 3: 305 = 1 + 84 + 220 = 20 + 120 + 165 = 56 + 84 + 165.

Martin Ehrenstein, Table of n, a(n) for n = 3..52
Eric Weisstein's World of Mathematics, Pyramidal Number

Cf. A080851, A350210, A350405.

a(10)-a(22) from Michael S. Branicky, Dec 29 2021

a(23)-a(36) from Martin Ehrenstein, Jan 14 2022

A350207 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

25, 65, 144, 305, 456, 622, 731, 1006, 1434, 1499, 1711, 1806, 2446, 2742, 3001, 3051, 3544, 3699, 3962, 4345, 5362, 5039, 5756, 5712, 6251, 6655, 7399, 7698, 7591, 8304, 8673, 9241, 9362, 9299, 10312, 10606, 11121, 10736, 12113, 12737, 12934

Offset: 3

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Polygonal Number

Cf. A057145, A097563, A274046, A350196, A350197, A350198, A350199, A350209, A350210.

A350209 a(n) is the smallest positive integer which can be represented as the sum of distinct centered n-gonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

65, 151, 330, 316, 515, 645, 888, 824, 1017, 1348, 1474, 1614, 1655, 2006, 2233, 2255, 2779, 2805, 2882, 2865, 3364, 3653, 3930, 4035, 4325, 4765, 4675, 5016, 4904, 5446, 5913, 5990, 6061, 6954, 6850, 7681, 8313, 7846, 7591, 9035, 8736

Offset: 3

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Cf. A101321, A350195, A350203, A350204, A350207, A350210.

A359321 a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.

Original entry on oeis.org

2300, 6201, 8125, 6391

Offset: 3

Ilya Gutkovskiy, Dec 25 2022

			For n = 3: 2300 = 1 + 969 + 1330 = 56 + 220 + 2024 = 165 + 364 + 1771.
For n = 4: 6201 = 1 + 91 + 1785 + 4324 = 1 + 285 + 1015 + 4900 = 30 + 140 + 506 + 5525 = 91 + 819 + 1496 + 3795.

Eric Weisstein's World of Mathematics, Pyramidal Number

Cf. A080851, A350210, A350397, A350423.

cp's OEIS Frontend

A350397 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if no such number exists.

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A350207 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such integer exists.

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A350209 a(n) is the smallest positive integer which can be represented as the sum of distinct centered n-gonal numbers in exactly n ways, or 0 if no such integer exists.

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Author

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A359321 a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.

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