cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A121550 Number of ordered ways of writing n as a sum of three Fibonacci numbers (only one 1 is considered as a Fibonacci number).

Original entry on oeis.org

0, 0, 1, 3, 6, 7, 9, 9, 10, 9, 12, 12, 9, 9, 10, 12, 12, 12, 12, 6, 9, 6, 12, 13, 9, 12, 12, 9, 12, 6, 12, 6, 0, 9, 6, 9, 15, 9, 13, 9, 6, 12, 9, 12, 9, 0, 12, 6, 6, 12, 0, 6, 0, 0, 9, 6, 9, 12, 9, 15, 9, 6, 13, 6, 9, 6, 0, 12, 9, 9, 12, 0, 9, 0, 0, 12, 6, 6, 6, 0, 12, 0, 0, 6, 0, 0, 0, 0, 9, 6, 9, 12
Offset: 1

Views

Author

Emeric Deutsch, Aug 07 2006

Keywords

Examples

			a(6)=7 because we have 6=1+2+3=1+3+2=2+1+3=2+3+1=3+1+2=3+2+1=2+2+2.

Links

Crossrefs

Cf. A000045, A121548, A121549, A357688, A357690, A357691.

Programs

  • Maple
    with(combinat): g:=sum(z^fibonacci(i),i=2..30)^3: gser:=series(g,z=0,130): seq(coeff(gser,z,n),n=1..126);

Formula

G.f.: (Sum_{i>=2} x^Fibonacci(i))^3.
a(n) = A121548(n,3).

A121549 Number of ordered ways of writing n as a sum of two Fibonacci numbers (only one 1 is considered as a Fibonacci number).

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 2, 2, 2, 3, 2, 0, 2, 2, 2, 3, 0, 2, 0, 0, 2, 2, 2, 2, 0, 3, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0
Offset: 1

Views

Author

Emeric Deutsch, Aug 07 2006

Keywords

Examples

			a(6)=3 because we have 6=1+5=3+3=5+1.

Links

Crossrefs

Cf. A000045, A121548, A121550, A357688, A357690, A357691.

Programs

  • Maple
    with(combinat): g:=sum(z^fibonacci(i),i=2..30)^2: gser:=series(g,z=0,130): seq(coeff(gser,z,n),n=1..126);

Formula

G.f.: (Sum_{i>=2} x^Fibonacci(i))^2.
a(n) = A121548(n,2).

A357688 Number of ways to write n as an ordered sum of four positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 4, 10, 16, 23, 28, 34, 36, 43, 48, 50, 48, 50, 56, 58, 64, 67, 60, 58, 52, 64, 64, 70, 68, 70, 76, 70, 72, 79, 60, 60, 48, 58, 68, 60, 84, 80, 64, 82, 64, 82, 88, 66, 76, 66, 64, 84, 60, 79, 60, 24, 60, 36, 60, 74, 48, 88, 76, 72, 96, 68, 88, 76, 48, 82, 60, 70
Offset: 4

Views

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

Links

Crossrefs

Cf. A000045, A076739, A121548, A121549, A121550, A319397, A357690, A357691.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^4.
a(n) = A121548(n,4).

A357691 Number of ways to write n as an ordered sum of six positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 6, 21, 50, 96, 156, 231, 312, 405, 506, 621, 726, 828, 930, 1041, 1160, 1290, 1422, 1520, 1590, 1677, 1766, 1887, 1980, 2106, 2196, 2310, 2426, 2550, 2670, 2706, 2700, 2736, 2756, 2850, 2916, 3071, 3156, 3186, 3296, 3396, 3510, 3621, 3636, 3765, 3720, 3840, 3966, 4010
Offset: 6

Views

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

Links

Crossrefs

Cf. A000045, A076739, A121548, A121549, A121550, A319399, A357688, A357690.

Programs

  • Mathematica
    nmax = 54; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^6.
a(n) = A121548(n,6).

A358005 Number of partitions of n into 5 distinct positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 1, 3, 2, 2, 2, 1, 2
Offset: 19

Views

Author

Ilya Gutkovskiy, Oct 24 2022

Keywords

Links

Crossrefs

Cf. A000045, A000119, A319398, A357690, A357722, A357731, A357732, A358006, A358007, A358008.

Programs

  • Maple
    G:= mul(1+t*x^combinat:-fibonacci(k),k=2..21):
S:= coeff(expand(G),t,5):
seq(coeff(S,x,i),i=19..110); # Robert Israel, Jan 06 2023

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

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

Crossrefs

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

Programs

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

Formula

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

Views

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

Crossrefs

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

Programs

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

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^8.
a(n) = A121548(n,8).

A357717 Number of ways to write n as an ordered sum of nine positive Fibonacci numbers (with a single type of 1).

Original entry on oeis.org

1, 9, 45, 156, 423, 954, 1878, 3321, 5409, 8251, 11979, 16686, 22446, 29250, 37134, 46107, 56259, 67671, 80407, 94338, 109269, 125118, 141930, 159723, 178608, 198522, 219510, 241338, 264438, 288810, 314550, 341010, 367785, 394596, 421443, 448650, 476614, 505404, 534978
Offset: 9

Views

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

Crossrefs

Cf. A000045, A076739, A121548, A121549, A121550, A319402, A357688, A357690, A357691, A357694, A357716.

Programs

  • Mathematica
    nmax = 47; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^9.
a(n) = A121548(n,9).

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

Views

Author

Ilya Gutkovskiy, Oct 11 2022

Keywords

Crossrefs

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

Programs

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

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^10.
a(n) = A121548(n,10).
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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