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 1-4 of 4 results.

A098641 Number of partitions of the n-th Fibonacci number into Fibonacci numbers.

Original entry on oeis.org

1, 1, 1, 2, 3, 6, 14, 41, 157, 803, 5564, 53384, 718844, 13783708, 380676448, 15298907733, 902438020514, 78720750045598, 10220860796171917, 1986422867300209784, 580763241873718042562, 256553744608217295298827, 171912553856721407543178940, 175350753369071026461010505478
Offset: 0

Views

Author

Marcel Dubois de Cadouin (dubois.ml(AT)club-internet.fr), Oct 27 2004

Keywords

Comments

a(n) = A003107(A000045(n)).

Examples

			n=6: A000045(6)=8, a(6) = #{8, 5+3, 5+2+1, 5+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 14; the other partitions of 8 into parts with at least one non-Fibonacci number: 7+1, 6+2, 6+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1 and 4+1+1+1+1.

Links

Crossrefs

Cf. A000041, A000045, A065033, A072214, A098642, A098643, A098644, A319503.

Programs

  • Mathematica
    cl = CoefficientList[ Series[1/Product[(1 - x^Fibonacci[i]), {i, 2, 21}], {x, 0, 10950}], x]; cl[[ Table[ Fibonacci[i] + 1, {i, 21}] ]] (* Robert G. Wilson v, Apr 25 2005 *)

Formula

a(n) = A098642(n) + A098643(n) + A098644(n).

Extensions

Corrected and extended by Reinhard Zumkeller, Apr 24 2005
a(15)-a(21) from Robert G. Wilson v, Apr 25 2005
Entry revised by N. J. A. Sloane, Mar 29 2006
a(0), a(22)-a(23) from Alois P. Heinz, Sep 20 2018

A072241 Number of distinct partitions of Fibonacci(n).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 6, 18, 76, 512, 6378, 173682, 12769602, 3328423936, 4338469000206, 43848229368772905, 5999189517441089061374, 22578203777383772718280932410, 5759108897879943749493986821813718586, 313503492905074747917062873989282073311633745920
Offset: 0

Views

Author

Robert G. Wilson v, Jul 06 2002

Keywords

Links

Crossrefs

Cf. A000009, A000045, A072214.

Programs

  • Maple
    F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= n-> g(F(n)):
seq(a(n), n=0..18);  # Alois P. Heinz, Apr 06 2021
  • Mathematica
    Table[ PartitionsQ[ Fibonacci[n]], {n, 1, 19}]

Formula

a(n) = A000009(A000045(n)).

Extensions

a(0)=1 prepended and a(19) added by Alois P. Heinz, Apr 06 2021

A152479 Products of partition numbers of Fibonacci numbers.

Original entry on oeis.org

1, 1, 1, 2, 6, 42, 924, 93324, 73912608, 909864204480, 410599878740916480, 20528320742539954765344000, 462721784193718931971550165554080000, 28136323479948516473366521258111350797954332320000
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

Keywords

Links

Crossrefs

Cf. A000041, A000045, A072214.

Programs

  • Maple
    A072214:= [seq(combinat:-numbpart(combinat:-fibonacci(n)),n=1..20)]:
seq(mul(A072214[i],i=1..n-1),n=1..20); # Robert Israel, Oct 20 2016
  • Mathematica
    f[n_]:=Fibonacci[n];p[n_]:=PartitionsP[f[n]];a[n_]:=Product[p[i],{i,1,n}];

Formula

a(n) = Prod_{1<=j<=n-1} A072214(j). - Robert Israel, Oct 20 2016

A272891 Number of partitions of Lucas(n).

Original entry on oeis.org

2, 1, 3, 5, 15, 56, 385, 4565, 124754, 9289091, 2552338241, 3646072432125, 42748078035954696, 7274403582551733377346, 37285884524590579748861394570, 14531841772646818920248481411605550560, 1400135408797883233268006240578157606704308520406
Offset: 0

Views

Author

Vincenzo Librandi, May 09 2016

Keywords

Examples

			a(4) = A000041(A000032(4)) = 15 because there are fifteen partitions of Lucas(4) = 7, namely: {7}, {6,1}, {5,2}, {5,1,1}, {4,3}, {4,2,1}, {4,1,1,1}, {3,3,1}, {3,2,2}, {3,2,1,1}, {3,1,1,1,1}, {2,2,2,1}, {2,2,1,1,1}, {2,1,1,1,1,1}, {1,1,1,1,1,1,1}.

Links

Crossrefs

Cf. A000032, A000041, A072214, A100845.

Programs

  • Magma
    [NumberOfPartitions(Lucas(n)): n in [0..18]];
  • Mathematica
    Table[PartitionsP[LucasL[n]], {n, 0, 18}]

Formula

a(n) = A000041(A000032(n)).

Extensions

Edited by Bruno Berselli, May 09 2016
Showing 1-4 of 4 results.

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

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