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.

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A111427 Tribonacci(tetranacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 24, 1705, 8646064, 120879712950776, 6984325661199418257711189170, 2037364946117781220616409939151494028465982215442078400
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Links

Crossrefs

Cf. A000045, A000073, A000078, A007570.

Programs

  • Maple
    a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^((<<0|1|0|0>,
        <0|0|1|0>, <0|0|0|1>, <1|1|1|1>>^n)[1, 4]))[1, 3]:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 07 2018

Formula

a(n) = A000073(A000078(n)).

A111428 Tribonacci(pentanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 24, 3136, 29249425, 2544489349890656, 10469303814509319059584520878072, 52390584919058211443518140875804297526718993867687450278537778
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Links

Crossrefs

Cf. A000045, A000073, A001591, A007570.

Programs

  • Maple
    a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^((<<0|1|0|0|0>,
        <0|0|1|0|0>, <0|0|0|1|0>, <0|0|0|0|1>, <1|1|1|1|1>>^n)[1, 5]))[1, 3]:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 07 2018

Formula

a(n) = A000073(A001591(n)).

A111429 Tribonacci(hexanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 2, 24, 3136, 53798080, 8607945812375585, 220376367601372354229355484029120, 78531983922879942351416192215114163135375656803468317366190276600
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Links

Crossrefs

Cf. A000045, A000073, A001592, A007570.

Programs

  • Maple
    a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^((<<0|1|0|0|0|0>, <0|0|1|0|0|0>,
    <0|0|0|1|0|0>, <0|0|0|0|1|0>, <0|0|0|0|0|1>, <1|1|1|1|1|1>>^n)[1, 6]))[1, 3]:
seq(a(n), n=0..14);  # Alois P. Heinz, Nov 07 2018

Formula

a(n) = A000073(A001592(n)).

A113597 a(n) = F(F(n+1)) - F(F(n)), where F() = Fibonacci numbers.

Original entry on oeis.org

1, 0, 0, 1, 3, 16, 212, 10713, 5691941, 139578159558, 1779979276420851744, 555565404222512714988011077619, 2211236406303914545143847565520581298983941196845, 2746979206949941983182302875626552882765513393050066744028390937621757948751904
Offset: 0

Views

Author

Amarnath Murthy, Nov 07 2005

Keywords

Links

Crossrefs

Cf. A000045. First differences of A007570.

Programs

  • Maple
    F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> F(F(n+1)) - F(F(n)):
seq(a(n), n=0..13);  # Alois P. Heinz, Nov 07 2018
  • PARI
    F=fibonacci; a(n) = F(F(n+1)) - F(F(n)); \\ Michel Marcus, Sep 16 2013

Extensions

Better description from Jonathan Vos Post, Nov 10 2005
Edited by N. J. A. Sloane, Nov 11 2005
a(0)=1 prepended by Alois P. Heinz, Nov 07 2018

A130589 a(n) = F(F(n)-1), where F(n) = A000045(n) (the Fibonacci numbers).

Original entry on oeis.org

1, 0, 0, 1, 1, 3, 13, 144, 6765, 3524578, 86267571272, 1100087778366101931, 343358302784187294870275058337, 1366619256256991435939546543402365995473880912459, 1697726516284295515651670644354144400761613511040643009353262085480136081475307
Offset: 0

Views

Author

Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Jun 16 2007

Keywords

Examples

			a(1)=F(F(1)-1)=F(0)=0;
a(2)=F(F(2)-1)=F(0)=0;
a(3)=F(F(3)-1)=F(1)=1;
a(4)=F(F(4)-1)=F(2)=1;
a(5)=F(F(5)-1)=F(4)=3;

Links

Crossrefs

Cf. A000045.
Cf. A007570.

Programs

  • Maple
    with(combinat): a:= proc(n) fibonacci(fibonacci(n)-1) end proc: seq(a(n), n = 0 .. 14);
# second Maple program:
F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> F(F(n)-1):
seq(a(n), n=0..14);  # Alois P. Heinz, Nov 07 2018
  • Mathematica
    Fibonacci[Fibonacci[Range[15]]-1] (* Harvey P. Dale, Feb 18 2018 *)

Extensions

Edited by Emeric Deutsch, Jul 10 2007
a(0)=1 prepended by Alois P. Heinz, Nov 07 2018

A356550 a(n) is the period of {F(F(k)) mod n, k >= 0}, where F denotes the Fibonacci numbers (A000045).

Original entry on oeis.org

1, 4, 12, 24, 60, 12, 24, 24, 24, 60, 60, 24, 48, 24, 60, 24, 24, 24, 24, 120, 24, 60, 24, 24, 300, 48, 24, 24, 48, 60, 120, 24, 60, 24, 120, 24, 18, 24, 48, 120, 60, 24, 60, 120, 120, 24, 48, 24, 48, 300, 24, 48, 72, 24, 60, 24, 24, 48, 42, 120, 120, 120, 24
Offset: 1

Views

Author

Rémy Sigrist, Aug 11 2022

Keywords

Comments

F(F(k)) mod n = F(F(k mod pi(pi(n))) mod pi(n)) mod n (where pi = A001175), so F(F(k)) mod n is periodic and the sequence is well defined.

Examples

			For n = 6:
- A001175(A001175(6)) = A001175(24) = 24,
- the values of F(F(k)) mod 6 for k = 0..23 are:
          0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1, 0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1
- we see that F(F(k)) mod 6 = F(F(k+12)) mod 6,
- so a(6) = 12.

Links

Crossrefs

Cf. A000045, A001175, A007570.

Programs

  • PARI
    See Links section.

Formula

a(n) divides A001175(A001175(n)).

A111430 Tribonacci(heptanacci(n)).

Original entry on oeis.org

0, 0, 1, 2, 24, 3136, 53798080, 15832480722303616, 745527911414639917440582097294401, 1653079675982713719400420113305863285438472194540328413077493166464
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			Heptanacci(10) = A066178(10) = 504, so tribonacci(heptanacci(10)) =
A000073(504) ~ 4.4 * 10^133.

Crossrefs

Cf. A000073, A066178, A007570.

Formula

a(n) = A000073(A066178(n)).

A111432 Fibonacci(tetranacci(n)).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 3, 21, 610, 514229, 225851433717, 16641027750620563662096, 13180872826374098837632191485015125807374171, 284812298108489611757988937681460995615380088782304890986477195645969271404032323901
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(tetranacci(0)) = A000045(A000078(0)) = A000045(0) = 0.
a(1) = Fibonacci(tetranacci(1)) = A000045(A000078(1)) = A000045(0) = 0.
a(2) = Fibonacci(tetranacci(2)) = A000045(A000078(2)) = A000045(0) = 0.
a(3) = Fibonacci(tetranacci(3)) = A000045(A000078(3)) = A000045(1) = 1.
a(4) = Fibonacci(tetranacci(4)) = A000045(A000078(4)) = A000045(1) = 1.
a(5) = A000045(A000078(5)) = A000045(2) = 1.
a(6) = A000045(A000078(6)) = A000045(4) = 3.
a(7) = A000045(A000078(7)) = A000045(8) = 21.
a(8) = A000045(A000078(8)) = A000045(15) = 610.
a(9) = A000045(A000078(9)) = A000045(29) = 514229.
a(10) = A000045(A000078(10)) = A000045(56) = 225851433717.

Crossrefs

Cf. A000045, A000078, A066178, A007570.

Programs

  • Mathematica
    Fibonacci[LinearRecurrence[{1,1,1,1},{0,0,0,1},14]] (* Harvey P. Dale, Aug 03 2017 *)

Formula

a(n) = A000045(A000078(n)).

A111433 Fibonacci(pentanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 3, 21, 987, 1346269, 2504730781961, 5358359254990966640871840, 9366947731425726508977331996039353971111632790877, 4176188314410464025148116525118839856571907649518456624120477965205524606115754507996484677228773
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(pentanacci(0)) = A000045(A001591(0)) = A000045(0) = 0.
a(1) = Fibonacci(pentanacci(1)) = A000045(A001591(1)) = A000045(0) = 0.
a(2) = Fibonacci(pentanacci(2)) = A000045(A001591(2)) = A000045(0) = 0.
a(3) = Fibonacci(pentanacci(3)) = A000045(A001591(3)) = A000045(0) = 0.
a(4) = Fibonacci(pentanacci(4)) = A000045(A001591(4)) = A000045(1) = 1.
a(5) = Fibonacci(pentanacci(5)) = A000045(A001591(5)) = A000045(1) = 1.
a(6) = Fibonacci(pentanacci(6)) = A000045(A001591(6)) = A000045(2) = 1.
a(7) = A000045(A001591(7)) = A000045(4) = 3.
a(8) = A000045(A001591(8)) = A000045(8) = 21.
a(9) = A000045(A001591(9)) = A000045(16) = 987.

Crossrefs

Cf. A000045, A001591, A066178, A007570.

Formula

a(n) = A000045(A001591(n)).

A111435 a(n) = Fibonacci(hexanacci(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 3, 21, 987, 2178309, 6557470319842, 59425114757512643212875125, 3016128079338728432528443992613633888712980904400501
Offset: 0

Views

Author

Jonathan Vos Post, Nov 13 2005

Keywords

Examples

			a(0) = Fibonacci(hexanacci(0)) = A000045(A001592(0)) = A000045(0) = 0.
a(1) = Fibonacci(hexanacci(1)) = A000045(A001592(1)) = A000045(0) = 0.
a(2) = Fibonacci(hexanacci(2)) = A000045(A001592(2)) = A000045(0) = 0.
a(3) = Fibonacci(hexanacci(3)) = A000045(A001592(3)) = A000045(0) = 0.
a(4) = Fibonacci(hexanacci(4)) = A000045(A001592(4)) = A000045(0) = 0.
a(5) = Fibonacci(hexanacci(5)) = A000045(A001592(5)) = A000045(1) = 1.
a(6) = Fibonacci(hexanacci(6)) = A000045(A001592(6)) = A000045(1) = 1.
a(7) = Fibonacci(hexanacci(7)) = A000045(A001592(7)) = A000045(2) = 1.
a(8) = A000045(A001592(8)) = A000045(4) = 3.
a(9) = A000045(A001592(9)) = A000045(8) = 21.
a(10) = A000045(A001592(10)) = A000045(16) = 987.
a(11) = A000045(A001592(11)) = A000045(32) = 2178309.
a(12) = A000045(A001592(12)) = A000045(63) = 6557470319842.

Crossrefs

Cf. A000045, A001592, A066178, A007570.

Programs

  • Maple
    b:= proc(n) option remember; `if`(n<5, 0,
      `if`(n=5, 1, add(b(n-j), j=1..6)))
    end:
a:= n-> (<<0|1>, <1|1>>^b(n))[1,2]:
seq(a(n), n=0..14);  # Alois P. Heinz, Aug 09 2018

Formula

a(n) = A000045(A001592(n)).
Previous Showing 11-20 of 21 results. Next

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

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