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.

A110062 Expansion of (1 - x + 2*x^2) / (1 - x^3 + x^4).

Original entry on oeis.org

1, -1, 2, 1, -2, 3, -1, -3, 5, -4, -2, 8, -9, 2, 10, -17, 11, 8, -27, 28, -3, -35, 55, -31, -32, 90, -86, -1, 122, -176, 85, 123, -298, 261, 38, -421, 559, -223, -459, 980, -782, -236, 1439, -1762, 546, 1675, -3201, 2308, 1129, -4876, 5509, -1179, -6005, 10385, -6688, -4826, 16390, -17073, 1862, 21216
Offset: 0

Views

Author

Creighton Dement, Jul 10 2005

Keywords

Comments

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110061-A110064).

Links

Crossrefs

Cf. A110061, A110063, A110064.

Programs

  • Maple
    seriestolist(series((1-x+2*x^2)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4ibaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
  • PARI
    Vec((1 - x + 2*x^2) / (1 - x^3 + x^4) + O(x^55)) \\ Colin Barker, May 11 2019

Formula

a(n) = a(n-3) - a(n-4) for n>3. - Colin Barker, May 11 2019

A110063 Expansion of -(3 - x + 2*x^2) / (1 - x^3 + x^4).

Original entry on oeis.org

-3, 1, -2, -3, 4, -3, -1, 7, -7, 2, 8, -14, 9, 6, -22, 23, -3, -28, 45, -26, -25, 73, -71, 1, 98, -144, 72, 97, -242, 216, 25, -339, 458, -191, -364, 797, -649, -173, 1161, -1446, 476, 1334, -2607, 1922, 858, -3941, 4529, -1064, -4799, 8470, -5593, -3735, 13269, -14063, 1858, 17004, -27332, 15921, 15146, -44336
Offset: 0

Views

Author

Creighton Dement, Jul 10 2005

Keywords

Comments

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110061-64).

Links

Crossrefs

Cf. A110061, A110062, A110064.

Programs

  • Maple
    seriestolist(series(-(3-x+2*x^2)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4jbaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
  • PARI
    Vec(-(3 - x + 2*x^2) / (1 - x^3 + x^4) + O(x^45)) \\ Colin Barker, May 11 2019

Formula

a(n) = a(n-3) - a(n-4) for n>3. - Colin Barker, May 11 2019

A110061 Expansion of x^2*(-3+4*x)/(1-x^3+x^4).

Original entry on oeis.org

0, 0, -3, 4, 0, -3, 7, -4, -3, 10, -11, 1, 13, -21, 12, 12, -34, 33, 0, -46, 67, -33, -46, 113, -100, -13, 159, -213, 87, 172, -372, 300, 85, -544, 672, -215, -629, 1216, -887, -414, 1845, -2103, 473, 2259, -3948, 2576, 1786, -6207, 6524, -790, -7993, 12731, -7314, -7203, 20724, -20045, 111, 27927, -40769, 20156
Offset: 0

Views

Author

Creighton Dement, Jul 10 2005

Keywords

Comments

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110062-64).

Links

Crossrefs

Cf. A110062, A110063, A110064.

Programs

  • Maple
    seriestolist(series(x^2*(-3+4*x)/(1-x^3+x^4), x=0,30)); -or- 4tesseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
  • Mathematica
    CoefficientList[Series[x^2(-3+4x)/(1-x^3+x^4),{x,0,100}],x] (* or *) LinearRecurrence[{0,0,1,-1},{0,0,-3,4},100] (* Harvey P. Dale, Nov 04 2021 *)
Showing 1-3 of 3 results.

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