A342254 -id:A342254 - cp's OEIS frontend

A342250 Number of ways to write n as an ordered sum of seven powers of 2.

1, 7, 21, 42, 77, 126, 168, 218, 294, 357, 427, 546, 637, 672, 756, 840, 854, 966, 1134, 1218, 1302, 1408, 1484, 1554, 1680, 1827, 1995, 2002, 1925, 2016, 1988, 1904, 2142, 2352, 2282, 2352, 2534, 2520, 2604, 2954, 3080, 3276, 3262, 3234, 3150, 3248, 3164, 3402, 3640

Offset: 7

Ilya Gutkovskiy, Mar 07 2021

Robert Israel, Table of n, a(n) for n = 7..10000

Cf. A000079, A023359, A073267, A151759, A151760, A151761, A151762, A209229, A342247, A342251, A342252, A342254.

N:= 100:
S:= add(x^(2^j),j=0..ilog2(N-6))^7:
[seq](coeff(S,x,j),j=7..N); # Robert Israel, Feb 26 2023

nmax = 55; CoefficientList[Series[Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

G.f.: ( Sum_{k>=0} x^(2^k) )^7.

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

Original entry on oeis.org

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.

A342252 Number of ways to write n as an ordered sum of nine powers of 2.

Original entry on oeis.org

1, 9, 36, 93, 198, 378, 624, 927, 1341, 1849, 2412, 3159, 4074, 4950, 5904, 7032, 8010, 9018, 10488, 11970, 13356, 15108, 16848, 18315, 20085, 22257, 24444, 26671, 28674, 30510, 32208, 33282, 34974, 37590, 39384, 40986, 43668, 45468, 46512, 49620, 53298, 55890, 59304, 62442

Offset: 9

Ilya Gutkovskiy, Mar 07 2021

nonn

Cf. A000079, A023359, A073267, A151759, A151760, A151761, A151762, A209229, A342249, A342250, A342251, A342254.

nmax = 52; CoefficientList[Series[Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

G.f.: ( Sum_{k>=0} x^(2^k) )^9.

cp's OEIS Frontend

A342250 Number of ways to write n as an ordered sum of seven powers of 2.

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

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Maple

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A342252 Number of ways to write n as an ordered sum of nine powers of 2.

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