A357717 -id:A357717 - cp's OEIS frontend

A357694 Number of ways to write n as an ordered sum of seven positive Fibonacci numbers (with a single type of 1).

1, 7, 28, 77, 168, 308, 504, 750, 1050, 1400, 1813, 2261, 2737, 3227, 3753, 4312, 4921, 5579, 6230, 6832, 7413, 8008, 8652, 9289, 9996, 10654, 11361, 12061, 12853, 13657, 14357, 14924, 15393, 15869, 16408, 16933, 17689, 18319, 18949, 19537, 20244, 21049, 21728

Offset: 7

Ilya Gutkovskiy, Oct 10 2022

nonn

Cf. A000045, A076739, A121548, A121549, A121550, A319400, A357688, A357690, A357691, A357716, A357717.

nmax = 49; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

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

a(n) = A121548(n,7).

A357716 Number of ways to write n as an ordered sum of eight positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 8, 36, 112, 274, 560, 1008, 1640, 2479, 3536, 4844, 6392, 8170, 10136, 12308, 14680, 17291, 20160, 23248, 26440, 29674, 32992, 36456, 40040, 43834, 47712, 51752, 55840, 60250, 64856, 69560, 74088, 78331, 82440, 86500, 90616, 95074, 99568, 104188, 108528, 113304

Offset: 8

Ilya Gutkovskiy, Oct 10 2022

nonn

Cf. A000045, A076739, A121548, A121549, A121550, A319401, A357688, A357690, A357691, A357694, A357717.

nmax = 48; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

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

a(n) = A121548(n,8).

A357730 Number of ways to write n as an ordered sum of ten positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 10, 55, 210, 625, 1542, 3300, 6310, 11040, 17980, 27673, 40660, 57475, 78520, 104175, 134742, 170620, 212220, 260035, 314290, 374933, 441790, 514855, 594210, 680070, 772582, 871920, 977790, 1090680, 1210960, 1339417, 1475340, 1618020, 1766080, 1918785, 2076012

Offset: 10

Ilya Gutkovskiy, Oct 11 2022

nonn

Cf. A000045, A076739, A121548, A121549, A121550, A319403, A357688, A357690, A357691, A357694, A357716, A357717.

nmax = 45; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^10.

a(n) = A121548(n,10).

cp's OEIS Frontend

A357694 Number of ways to write n as an ordered sum of seven positive Fibonacci numbers (with a single type of 1).

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A357716 Number of ways to write n as an ordered sum of eight positive Fibonacci numbers (with a single type of 1).

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Mathematica

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A357730 Number of ways to write n as an ordered sum of ten positive Fibonacci numbers (with a single type of 1).

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Mathematica

Formula