A089048 -id:A089048 - cp's OEIS frontend

A089049 Number of ways of writing n as a sum of exactly 4 powers of 2.

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

Offset: 0

N. J. A. Sloane, Dec 03 2003

nonn

The powers do not need to be distinct.

Alois P. Heinz, Table of n, a(n) for n = 0..20000

A column of A089052. Cf. A036987, A075897, A089048, A089050, A089051, A089053.

A089050 Number of ways of writing n as a sum of exactly 5 powers of 2.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 03 2003

nonn

The powers do not need to be distinct.

Alois P. Heinz, Table of n, a(n) for n = 0..65536

A column of A089052. Cf. A036987, A075897, A089048, A089049, A089051, A089053.

A089051 Number of ways of writing n as a sum of exactly 6 powers of 2.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 03 2003

nonn

The powers do not need to be distinct.

Alois P. Heinz, Table of n, a(n) for n = 0..65536

A column of A089052. Cf. A036987, A075897, A089048, A089049, A089050, A089053.

A342247 Number of partitions of n into seven powers of 2.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 4, 3, 4, 4, 4, 4, 5, 4, 6, 5, 6, 6, 7, 5, 8, 6, 7, 6, 8, 5, 7, 5, 7, 6, 9, 6, 9, 7, 9, 7, 11, 8, 10, 7, 10, 7, 10, 6, 11, 8, 10, 7, 12, 7, 10, 7, 11, 7, 10, 5, 9, 5, 8, 5, 10, 7, 10, 6, 11, 9, 12, 8, 14, 9, 11, 7, 13, 8, 12, 8, 14, 10, 13, 8, 15, 9, 13

Offset: 7

Ilya Gutkovskiy, Mar 07 2021

nonn

Column k=7 of A089052.

Cf. A000079, A000123, A018819, A075897, A089048, A089049, A089050, A089051, A209229, A319922, A342248, A342249, A342250.

A342248 Number of partitions of n into eight powers of 2.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 4, 5, 5, 6, 6, 7, 6, 8, 7, 8, 8, 10, 7, 10, 8, 9, 7, 10, 7, 10, 9, 11, 9, 12, 9, 13, 11, 14, 10, 14, 10, 13, 10, 14, 11, 15, 10, 15, 12, 15, 10, 17, 11, 14, 10, 15, 9, 13, 8, 14, 10, 14, 10, 16, 11, 16, 12, 18, 14, 18, 11, 18, 13, 17, 12, 20

Offset: 8

Ilya Gutkovskiy, Mar 07 2021

nonn

Column k=8 of A089052.

Cf. A000079, A000123, A018819, A075897, A089048, A089049, A089050, A089051, A209229, A319922, A342247, A342249, A342251.

A342249 Number of partitions of n into nine powers of 2.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 8, 7, 8, 8, 9, 8, 11, 10, 11, 10, 12, 9, 12, 10, 12, 10, 14, 11, 14, 12, 15, 13, 17, 14, 18, 14, 17, 13, 18, 14, 19, 15, 19, 15, 20, 15, 21, 17, 21, 14, 21, 15, 19, 13, 20, 14, 19, 14, 22, 16, 21, 16, 24, 18, 24, 18, 25

Offset: 9

Ilya Gutkovskiy, Mar 07 2021

nonn

Column k=9 of A089052.

Cf. A000079, A000123, A018819, A075897, A089048, A089049, A089050, A089051, A209229, A319922, A342247, A342248, A342252.

A347658 Number of partitions of n into at most 3 powers of 2.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A000079, A018819, A089048, A347659, A347660, A347661.

cp's OEIS Frontend

A089049 Number of ways of writing n as a sum of exactly 4 powers of 2.

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A089050 Number of ways of writing n as a sum of exactly 5 powers of 2.

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A089051 Number of ways of writing n as a sum of exactly 6 powers of 2.

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A342247 Number of partitions of n into seven powers of 2.

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A342248 Number of partitions of n into eight powers of 2.

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A342249 Number of partitions of n into nine powers of 2.

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A347658 Number of partitions of n into at most 3 powers of 2.

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