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 1-2 of 2 results.

A075876 Values of m for which A075825(m) = 1.

Original entry on oeis.org

0, 2, 4, 12, 52, 212, 852, 3412, 13652, 54612, 218452, 873812, 3495252, 13981012, 55924052, 223696212
Offset: 1

Views

Author

John W. Layman, Oct 16 2002

Keywords

Comments

For n > 4 it appears that a(n) = 4*a(n-1) + 4.
From Robert Israel, Nov 08 2016: (Start)
By induction, we have for k >= 0:
A075825((10*4^k-7)/3) = 2^(k+1)
A075825((10*4^k-4)/3) = 1
A075825((10*4^k-1)/3) = 2^(k+1)+1
A075825((20*4^k-8)/3) = 2^(k+1)-1
A075825((20*4^k-5)/3) = 2^(k+1)+1
A075825((20*4^k-1)/3) = 2^(k+1)
In particular, this sequence contains b(k) = (10*4^k-4)/3 which is the solution of b(k) = 4*b(k-1)+4 with b(0) = 2.
The only terms <= 2*10^7 that are not of that form are 0 and 4. (End)

Crossrefs

Cf. A075825.

Extensions

a(10)-a(14) from Robert Israel, Nov 08 2016
a(15)-a(16) from Sean A. Irvine, Mar 11 2025

A325055 a(0) = 0, a(1) = 1; a(2*n) = a(n-1) + a(n), a(2*n+1) = a(n+1) - a(n).

Original entry on oeis.org

0, 1, 1, 0, 2, -1, 1, 2, 2, -3, 1, 2, 0, 1, 3, 0, 4, -5, -1, 4, -2, 1, 3, -2, 2, 1, 1, 2, 4, -3, 3, 4, 4, -9, -1, 4, -6, 5, 3, -6, 2, 3, -1, 2, 4, -5, 1, 4, 0, -1, 3, 0, 2, 1, 3, 2, 6, -7, 1, 6, 0, 1, 7, 0, 8, -13, -5, 8, -10, 5, 3, -10, -2, 11, -1, -2
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 04 2019

Keywords

Links

Crossrefs

Cf. A001196 (positions of 0's), A002487, A005590, A075825.

Programs

  • Mathematica
    a[0] = 0; a[1] = 1; a[n_] := a[n] = If[EvenQ[n], a[(n - 2)/2] + a[n/2], a[(n + 1)/2] - a[(n - 1)/2]]; Table[a[n], {n, 0, 75}]

Formula

a(n) = Sum_{k=1..n} a(2*k-1) = Sum_{k=1..n} (-1)^(n-k) * a(2*k).
a(2^k) = 2^floor(k/2).
Showing 1-2 of 2 results.

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