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 1-3 of 3 results.

A111912 Expansion of x*(2 +3*x +x^2 -2*x^5 -x^7 -x^8)/((1-x)*(1+x)*(1-x^4+x^8)).

Original entry on oeis.org

0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1, 0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1, 0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1
Offset: 0

Views

Author

Creighton Dement, Aug 20 2005

Keywords

Comments

Sequence has period 24.

Links

Crossrefs

Cf. A085846, A111913, A111914, A111915.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 75);
Coefficients(R!( x*(2+3*x+x^2-2*x^5-x^7-x^8)/((1-x)*(1+x)*(1-x^4+x^8)) )); // G. C. Greubel, Feb 12 2021
  • Maple
    seq(coeff(series((x*(-2-3*x-x^2+2*x^5+x^7+x^8)/((x-1)*(x+1)*(x^8-x^4+1))),x,n+1),x,n),n=0..75); # Muniru A Asiru, Jun 06 2018
  • Mathematica
    LinearRecurrence[{0,1,0,1,0,-1,0,-1,0,1}, {0,2,3,3,3,5,4,6,3,5}, 75] (* G. C. Greubel, Feb 12 2021 *)
  • PARI
    Vec(x*(-2-3*x-x^2+2*x^5+x^7+x^8)/((x-1)*(x+1)*(x^8-x^4+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
  • Sage
    def A111912_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(2+3*x+x^2-2*x^5-x^7-x^8)/((1-x)*(1+x)*(1-x^4+x^8)) ).list()
A111912_list(75) # G. C. Greubel, Feb 12 2021

A111913 Expansion of x*(-2-3*x-x^2+x^7+x^8+2*x^4) / ((x-1)*(x+1)*(x^8-x^4+1)).

Original entry on oeis.org

0, 2, 3, 3, 3, 3, 6, 4, 5, 1, 5, 1, 4, -2, 1, -3, 1, -3, -2, -4, -1, -1, -1, -1, 0, 2, 3, 3, 3, 3, 6, 4, 5, 1, 5, 1, 4, -2, 1, -3, 1, -3, -2, -4, -1, -1, -1, -1, 0, 2, 3, 3, 3, 3, 6, 4, 5, 1, 5, 1, 4, -2, 1, -3, 1, -3, -2, -4, -1, -1, -1, -1, 0, 2, 3, 3, 3, 3, 6, 4, 5, 1, 5, 1, 4, -2, 1, -3, 1, -3, -2, -4, -1, -1, -1, -1, 0, 2, 3, 3
Offset: 0

Views

Author

Creighton Dement, Aug 20 2005

Keywords

Comments

It appears that (a(n)) has period 24.
The above conjecture is correct, since x^24 = 1 mod (x-1)*(x+1)*(x^8-x^4+1). - Charles R Greathouse IV, Feb 07 2013
Floretion Algebra Multiplication Program, FAMP Code: 4ibasesigcycsumseq[ + .5'i + .5j' + .5'ij' + .5e], sumtype: Y[8] = (int)Y[6] - (int)Y[7] + Y[8] + sum (internal program code); apart from initial term 0.

Links

Crossrefs

Cf. A111912, A111914, A111915, A085846.

Programs

  • Mathematica
    LinearRecurrence[{0,1,0,1,0,-1,0,-1,0,1},{0,2,3,3,3,3,6,4,5,1},120] (* Harvey P. Dale, Apr 14 2019 *)
  • PARI
    a(n)=[0,2,3,3,3,3,6,4,5,1,5,1,4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1][n%24+1] \\ Charles R Greathouse IV, Feb 07 2013
  • PARI
    concat(0, Vec(x*(2 + 3*x + x^2 - 2*x^4 - x^7 - x^8) / ((1 - x)*(1 + x)*(1 - x^4 + x^8)) + O(x^80))) \\ Colin Barker, May 18 2019

Formula

a(n) = a(n-2) + a(n-4) - a(n-6) - a(n-8) + a(n-10) for n>9. - Colin Barker, May 18 2019

A111914 Expansion of -x^2*(x^4-2*x^3+x^2-2*x+1)*(x+1)^2 / ((x-1)*(x^8-x^4+1)).

Original entry on oeis.org

0, 0, 1, 1, -1, -3, -4, -4, -5, -7, -9, -9, -8, -8, -9, -9, -7, -5, -4, -4, -3, -1, 1, 1, 0, 0, 1, 1, -1, -3, -4, -4, -5, -7, -9, -9, -8, -8, -9, -9, -7, -5, -4, -4, -3, -1, 1, 1, 0, 0, 1, 1, -1, -3, -4, -4, -5, -7, -9, -9, -8, -8, -9, -9, -7, -5, -4, -4, -3, -1, 1, 1, 0, 0, 1, 1, -1, -3, -4, -4, -5, -7, -9, -9, -8, -8, -9, -9, -7, -5, -4, -4
Offset: 0

Views

Author

Creighton Dement, Aug 20 2005

Keywords

Comments

It appears that (a(n)) has period 24.

Links

Crossrefs

Cf. A111912, A111913, A111915, A085846.

Programs

  • PARI
    concat([0,0], Vec(x^2*(1 + x)^2*(1 - 2*x + x^2 - 2*x^3 + x^4) / ((1 - x)*(1 - x^4 + x^8)) + O(x^40))) \\ Colin Barker, May 18 2019

Formula

a(n) = a(n-1) + a(n-4) - a(n-5) - a(n-8) + a(n-9) for n > 8. - Colin Barker, May 18 2019
Showing 1-3 of 3 results.

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