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.

A020951 a(2n+1)=a(n), a(2n)=a(n)+a(n-1).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A082498.

Programs

  • Haskell
    a020951 n = a020951_list !! n
a020951_list = 1 : ws where
   ws = 0 : 1 : concat (zipWith (\u v -> [u, u + v]) ws $ tail ws)
-- Reinhard Zumkeller, Jul 19 2013, Mar 13 2013

A214126 a(2n)=a(n-1)+a(n) and a(2n+1)=a(n+1) for n>=1, with a(0)=a(1)=1.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 4, 3, 5, 2, 5, 4, 6, 3, 7, 5, 8, 2, 7, 5, 7, 4, 9, 6, 10, 3, 9, 7, 10, 5, 12, 8, 13, 2, 10, 7, 9, 5, 12, 7, 12, 4, 11, 9, 13, 6, 15, 10, 16, 3, 13, 9, 12, 7, 16, 10, 17, 5, 15, 12, 17, 8, 20, 13, 21, 2, 15, 10, 12, 7, 17, 9, 16, 5, 14, 12
Offset: 0

Views

Author

Alex Ratushnyak, Jul 04 2012

Keywords

Comments

a(2^n) = A000045(n+2), a(2^n-1) = A000045(n+1). - Alois P. Heinz, Jul 06 2012

Examples

			a(2^n+1) = 2 because a(2) = 2 and a(2*n+1) = a(n+1).

Links

Crossrefs

Cf. A120562: same formula, seed {0,1}, first term removed.
Cf. A082498: same formula, seed {1,0}, first term removed.
Cf. A214127: same formula, seed {1,2}.
Cf. A000045.

Programs

  • Maple
    a:= proc(n) local r;
      a(n):= `if`(n<2, 1, `if`(irem(n, 2, 'r')=0, a(r-1)+a(r), a(r+1)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 06 2012
  • Mathematica
    a[0] = a[1] = 1;
a[n_] := a[n] = If[EvenQ[n], a[n/2-1] + a[n/2], a[(n-1)/2+1]];
Array[a, 100, 0] (* Jean-François Alcover, May 31 2019 *)
  • Python
    a = [1]*(77*2)
for n in range(1,77):
    a[2*n  ]=a[n-1]+a[n]
    a[2*n+1]=a[n+1]
    print(str(a[n-1]),end=',')

Formula

a(0) = a(1) = 1, for n>=1: a(2*n) = a(n-1)+a(n) and a(2*n+1) = a(n+1).

A214127 a(2n) = a(n-1) + a(n) and a(2n+1) = a(n+1) for n>=1, with a(0)=1, a(1)=2.

Original entry on oeis.org

1, 2, 3, 3, 5, 3, 6, 5, 8, 3, 8, 6, 9, 5, 11, 8, 13, 3, 11, 8, 11, 6, 14, 9, 15, 5, 14, 11, 16, 8, 19, 13, 21, 3, 16, 11, 14, 8, 19, 11, 19, 6, 17, 14, 20, 9, 23, 15, 24, 5, 20, 14, 19, 11, 25, 16, 27, 8, 24, 19, 27, 13, 32, 21, 34, 3, 24, 16, 19, 11, 27, 14, 25
Offset: 0

Views

Author

Alex Ratushnyak, Jul 04 2012

Keywords

Crossrefs

Cf. A120562: same formula, seed {0,1}, first term removed.
Cf. A082498: same formula, seed {1,0}, first term removed.
Cf. A214126: same formula, seed {1,1}.

Programs

  • Mathematica
    t = {1, 2}; Do[If[EvenQ[n], AppendTo[t, t[[n/2]] + t[[n/2 + 1]]], AppendTo[t, t[[(n + 3)/2]]]], {n, 2, 100}]; t (* T. D. Noe, Jul 11 2012 *)
  • Python
    a = [1]*(77*2)
a[1]=2
for n in range(1,77):
    a[2*n  ]=a[n-1]+a[n]
    a[2*n+1]=a[n+1]
    print(str(a[n-1]),end=',')

A342682 a(1) = 1; for n > 0: a(2*n) = -a(n+1), a(2*n+1) = a(n) + a(n+1).

Original entry on oeis.org

1, 0, 1, -1, 1, 1, 0, -1, 0, -1, 2, 0, 1, 1, -1, 0, -1, 1, -1, -2, 1, 0, 2, -1, 1, -1, 2, 1, 0, 0, -1, 1, -1, -1, 0, 1, 0, 2, -3, -1, -1, 0, 1, -2, 2, 1, 1, -1, 0, 1, 0, -2, 1, -1, 3, 0, 1, 0, 0, 1, -1, -1, 0, 1, 0, 1, -2, 0, -1, -1, 1, 0, 1, -2, 2, 3, -1, 1, -4
Offset: 1

Views

Author

George Beck, May 18 2021

Keywords

Examples

			a(2) = -a(2), so a(2) = 0; a(11) = a(5) + a(6) = 1 + 1 = 2.

Links

Crossrefs

Cf. A002487, A213369, A082498.

Programs

  • Mathematica
    a@1 = 1;
a@2 = 0;
a@n_ := -a[n/2 + 1] /; EvenQ@n;
a@n_ := a[1/2 (n - 1)] + a[1/2 (n - 1) + 1] /; OddQ@n;
a /@ Range[128]
Showing 1-4 of 4 results.

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