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.

A111665 Expansion of (-1+x+2*x^2+5*x^4+3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).

Original entry on oeis.org

1, 2, 3, 4, 5, 10, 23, 56, 141, 366, 955, 2496, 6529, 17090, 44739, 117124, 306629, 802762, 2101655, 5502200, 14404941, 37712622, 98732923, 258486144, 676725505, 1771690370, 4638345603, 12143346436, 31791693701, 83231734666, 217903510295
Offset: 0

Views

Author

Creighton Dement, Aug 14 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4ibaseisumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: Y[15],inty[ * ]

Links

Crossrefs

Cf. A111664, A111666.

Programs

  • Mathematica
    LinearRecurrence[{3, -1, 0, 1, -3, 1}, {1, 2, 3, 4, 5, 10}, 50] (* Paolo Xausa, Mar 09 2024 *)
  • PARI
    Vec((1 - x - 2*x^2 - 3*x^3 - 5*x^4) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x^2)) + O(x^35)) \\ Colin Barker, May 13 2019

Formula

a(n) = 3*a(n-1) - a(n-2) + a(n-4) - 3*a(n-5) + a(n-6) for n>5. - Colin Barker, May 13 2019

A109787 Expansion of -(1-x-2*x^2+11*x^4-3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).

Original entry on oeis.org

1, 2, 3, 4, 21, 58, 151, 392, 1037, 2718, 7115, 18624, 48769, 127682, 334275, 875140, 2291157, 5998330, 15703831, 41113160, 107635661, 281793822, 737745803, 1931443584, 5056584961, 13238311298, 34658348931, 90736735492, 237551857557
Offset: 0

Views

Author

Creighton Dement, Aug 14 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4tessumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: Y[15],inty[ * ]

Links

Crossrefs

Cf. A111664, A111666.

Programs

  • Mathematica
    CoefficientList[Series[-(1-x-2x^2+11x^4-3x^3)/((x-1)(x+1)(x^2-3x+1)(1+x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{3,-1,0,1,-3,1},{1,2,3,4,21,58},40] (* Harvey P. Dale, Jan 11 2020 *)
  • PARI
    Vec((1 - x - 2*x^2 - 3*x^3 + 11*x^4) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x^2)) + O(x^30)) \\ Colin Barker, May 16 2019

Formula

a(n) = 3*a(n-1) - a(n-2) + a(n-4) - 3*a(n-5) + a(n-6) for n>5. - Colin Barker, May 16 2019

A109786 Expansion of -(x+2*x^2+3*x^3-1+5*x^4)/((x+1)*(x^2-3*x+1)*(1+x^2)).

Original entry on oeis.org

1, 1, 1, 1, 1, 5, 13, 33, 85, 225, 589, 1541, 4033, 10561, 27649, 72385, 189505, 496133, 1298893, 3400545, 8902741, 23307681, 61020301, 159753221, 418239361, 1094964865, 2866655233, 7505000833, 19648347265, 51440040965, 134671775629
Offset: 0

Views

Author

Creighton Dement, Aug 14 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4jbaseksumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: Y[15],inty[ * ]

Links

Crossrefs

Cf. A111665, A111666.

Programs

  • Mathematica
    CoefficientList[Series[-(x+2x^2+3x^3-1+5x^4)/((x+1)(x^2-3x+1)(1+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{2,1,1,2,-1},{1,1,1,1,1},40] (* Harvey P. Dale, Apr 14 2015 *)

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(n)=2*a(n-1)+a(n-2)+a(n-3)+ 2*a(n-4)- a(n-5). - Harvey P. Dale, Apr 14 2015
Showing 1-3 of 3 results.

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