A307597 -id:A307597 - cp's OEIS frontend

A350288 a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.

1, 16, 37, 64, 83, 128, 177, 204, 270, 352, 430, 533, 632, 764, 893, 1102, 1256, 1443, 1630, 1855, 2141, 2384, 2699, 3053, 3378, 3753, 4176, 4620, 5068, 5570, 6107, 6654, 7253, 7904, 8526, 9241, 9975, 10699, 11533, 12401, 13301, 14189, 15179, 16233, 17286, 18412

Offset: 1

Ilya Gutkovskiy, Dec 23 2021

nonn

			For n = 2: 16 = 1 + 15 = 6 + 10.
For n = 3: 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.

Cf. A000217, A265134, A307597, A307598, A341021-A341027, A342326, A350241.

More terms from Jinyuan Wang, Dec 26 2021

A357070 Number of partitions of n into at most 2 distinct positive triangular numbers.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1

Offset: 0

Ilya Gutkovskiy, Oct 25 2022

nonn

Cf. A000217, A024940, A052343, A307597, A347730, A357071, A357072.

cp's OEIS Frontend

A350288 a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.

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A357070 Number of partitions of n into at most 2 distinct positive triangular numbers.

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Keywords

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