A342248 -id:A342248 - cp's OEIS frontend

A342251 Number of ways to write n as an ordered sum of eight powers of 2.

1, 8, 28, 64, 126, 224, 336, 464, 645, 840, 1044, 1344, 1666, 1904, 2192, 2528, 2730, 3024, 3528, 3920, 4284, 4768, 5168, 5488, 5965, 6552, 7140, 7616, 7834, 8176, 8400, 8352, 8862, 9632, 9800, 10080, 10788, 10976, 11152, 12208, 13090, 13664, 14392, 14672, 14868, 15008, 15344

Offset: 8

Ilya Gutkovskiy, Mar 07 2021

nonn

Robert Israel, Table of n, a(n) for n = 8..10000

Cf. A000079, A023359, A073267, A151759, A151760, A151761, A151762, A209229, A342248, A342250, A342252, A342254.

N:= 100:
S:= add(x^(2^j),j=0..ilog2(N-7))^8:
seq(coeff(S,x,j),j=8..N); # Robert Israel, Feb 26 2023

nmax = 54; CoefficientList[Series[Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

G.f.: ( Sum_{k>=0} x^(2^k) )^8.

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.

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.

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A342251 Number of ways to write n as an ordered sum of eight powers of 2.

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

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

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