A341027 -id:A341027 - cp's OEIS frontend

A341021 Number of partitions of n into 4 distinct nonzero triangular numbers.

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 1, 1, 0, 2, 1, 3, 0, 1, 2, 0, 2, 2, 1, 3, 2, 0, 2, 2, 2, 1, 3, 0, 4, 3, 1, 3, 2, 2, 3, 2, 1, 5, 3, 3, 2, 4, 1, 2, 5, 1, 5, 3, 2, 5, 3, 3, 4, 4, 3, 4, 6, 0, 6, 4, 2, 7, 4, 3, 5, 4, 3, 5, 5, 5, 4, 5, 5, 5, 8, 2, 6, 5, 1, 10, 5, 4, 7, 7, 4

Offset: 20

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A008438, A010054, A307597, A307598, A319814, A340949, A341022, A341023, A341024, A341025, A341026, A341027.

A341022 Number of partitions of n into 5 distinct nonzero triangular numbers.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 3, 0, 2, 2, 0, 1, 3, 2, 3, 2, 1, 2, 3, 2, 0, 5, 1, 3, 3, 2, 3, 2, 4, 2, 5, 2, 2, 6, 1, 4, 6, 1, 5, 6, 3, 4, 4, 4, 4, 5, 3, 5, 7, 6, 4, 8, 2, 5, 7, 3, 7, 7, 7, 5, 7, 6, 4, 12, 5, 4, 10, 3, 11, 9, 5, 9, 8, 5

Offset: 35

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A008439, A010054, A307597, A307598, A319815, A340950, A341021, A341023, A341024, A341025, A341026, A341027.

A341023 Number of partitions of n into 6 distinct nonzero triangular numbers.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 3, 1, 1, 3, 2, 1, 3, 2, 1, 3, 3, 1, 2, 3, 3, 5, 2, 2, 5, 1, 2, 5, 3, 4, 3, 5, 2, 4, 7, 1, 6, 4, 2, 8, 4, 5, 7, 4, 4, 6, 6, 4, 9, 6, 4, 8, 5, 6, 11, 8, 4, 9, 5, 8, 8, 9, 8, 9, 11

Offset: 56

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A008440, A010054, A307597, A307598, A319816, A340951, A341021, A341022, A341024, A341025, A341026, A341027.

A341024 Number of partitions of n into 7 distinct nonzero triangular numbers.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 1, 3, 0, 1, 1, 1, 3, 2, 2, 2, 2, 1, 2, 4, 0, 2, 4, 0, 3, 4, 3, 4, 3, 1, 4, 3, 3, 4, 4, 4, 2, 6, 3, 6, 6, 1, 6, 3, 3, 5, 9, 4, 4, 8, 2, 6, 9, 3, 9, 7, 4, 9, 6, 6, 10, 8, 5

Offset: 84

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A010054, A226252, A307597, A307598, A319817, A340952, A341021, A341022, A341023, A341025, A341026, A341027.

A341025 Number of partitions of n into 8 distinct nonzero triangular numbers.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 3, 1, 1, 3, 1, 1, 2, 1, 2, 4, 2, 2, 2, 0, 2, 5, 2, 1, 5, 2, 2, 4, 3, 4, 2, 3, 4, 3, 5, 1, 8, 4, 3, 8, 1, 4, 7, 2, 5, 7, 5, 6, 6, 4, 4, 10, 6

Offset: 120

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A007331, A010054, A307597, A307598, A319818, A340953, A341021, A341022, A341023, A341024, A341026, A341027.

A341026 Number of partitions of n into 9 distinct nonzero triangular numbers.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 3, 1, 0, 4, 1, 2, 1, 1, 1, 2, 3, 1, 2, 3, 0, 4, 3, 2, 3, 2, 2, 1, 4, 1, 6, 3, 1, 5, 2, 2, 7, 4, 2, 3, 4, 5, 5, 5, 4, 4, 6

Offset: 165

Ilya Gutkovskiy, Feb 02 2021

nonn

Cf. A000217, A010054, A226253, A307597, A307598, A319819, A340954, A341021, A341022, A341023, A341024, A341025, A341027.

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.

Original entry on oeis.org

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

cp's OEIS Frontend

A341021 Number of partitions of n into 4 distinct nonzero triangular numbers.

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A341022 Number of partitions of n into 5 distinct nonzero triangular numbers.

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A341023 Number of partitions of n into 6 distinct nonzero triangular numbers.

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A341024 Number of partitions of n into 7 distinct nonzero triangular numbers.

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A341025 Number of partitions of n into 8 distinct nonzero triangular numbers.

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A341026 Number of partitions of n into 9 distinct nonzero triangular numbers.

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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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