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.

A199930 Trisection 0 of A199803.

Original entry on oeis.org

1, -2, -1, 12, -10, -49, 112, 111, -710, 316, 3233, -5634, -9505, 40592, -1934, -204897, 264664, 717295, -2243578, -873336, 12543857, -11138050, -50210993, 119318436, 108054622, -743719745, 372976064, 3334358847, -6051013534, -9504084892, 42720535345, -4585483266, -212470264817, 287622301384
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2011

Keywords

Comments

Also trisection 1 of A199744, negated.

Links

Crossrefs

Cf. A199744, A199803.

Programs

  • Mathematica
    LinearRecurrence[{-1,-5,1,-1},{1,-2,-1,12},40] (* Harvey P. Dale, May 20 2025 *)
  • PARI
    Vec((1 - x + 2*x^2) / (1 + x + 5*x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Dec 27 2017

Formula

From Colin Barker, Dec 27 2017: (Start)
G.f.: (1 - x + 2*x^2) / (1 + x + 5*x^2 - x^3 + x^4).
a(n) = -a(n-1) - 5*a(n-2) + a(n-3) - a(n-4) for n>3.
(End)

A199931 Trisection 1 of A199803.

Original entry on oeis.org

-1, 2, 4, -15, -2, 79, -88, -294, 815, 488, -4769, 3438, 20080, -42527, -49666, 278943, -93220, -1308634, 2103343, 4067664, -15799793, -1126550, 82089836, -96324543, -299451394, 864290495, 454552096, -4979131422, 3870112831, 20615805880, -45400053553, -48829731594, 292575692408
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2011

Keywords

Links

Programs

  • Mathematica
    CoefficientList[ Series[(-1 +x +x^2)/(1 +x +5x^2 -x^3 +x^4), {x, 0, 30}], x] (* or *)
LinearRecurrence[{-1, -5, 1, -1}, {-1, 2, 4, -15}, 30] (* Robert G. Wilson v, Dec 27 2017 *)
  • PARI
    Vec(-(1 - x - x^2) / (1 + x + 5*x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Dec 27 2017

Formula

From Colin Barker, Dec 27 2017: (Start)
G.f.: -(1 - x - x^2) / (1 + x + 5*x^2 - x^3 + x^4).
a(n) = -a(n-1) - 5*a(n-2) + a(n-3) - a(n-4) for n>3.
(End)

A199802 G.f.: 1/(1-2*x+2*x^2-x^3+x^4).

Original entry on oeis.org

1, 2, 2, 1, -1, -4, -7, -8, -5, 3, 15, 27, 32, 22, -8, -55, -104, -128, -95, 17, 200, 399, 510, 405, -11, -721, -1525, -2024, -1708, -172, 2573, 5806, 8002, 7137, 1503, -9072, -22015, -31520, -29585, -9073, 31519, 83119, 123712, 121778, 47732, -107499, -312396, -483840, -498119, -233455, 357884, 1168399, 1885694, 2025929, 1090985, -1152593
Offset: 0

Views

Author

N. J. A. Sloane, Nov 10 2011

Keywords

Links

Crossrefs

The main sequences mentioned in the Hisrchhorn paper are A199802, A199803, A199744, A199804, A077961, A199805.

Programs

  • Mathematica
    CoefficientList[Series[1/(1-2x+2x^2-x^3+x^4),{x,0,60}],x] (* or *) LinearRecurrence[ {2,-2,1,-1},{1,2,2,1},60] (* Harvey P. Dale, May 11 2022 *)

A199928 Trisection 1 of A199802.

Original entry on oeis.org

2, -1, -8, 15, 22, -104, 17, 510, -721, -1708, 5806, 1503, -31520, 31519, 121778, -312396, -233455, 1885694, -1152593, -8196936, 16079050, 21867343, -109306936, 24246207, 528076766, -780482080, -1726348607, 6132589566, 1190594623, -32799408980, 34705374038, 124349675919, -331866549712
Offset: 0

Views

Author

N. J. A. Sloane, Nov 12 2011

Keywords

Comments

Also trisection 2 of A199803.

Links

Programs

  • Mathematica
    LinearRecurrence[{-1,-5,1,-1},{2,-1,-8,15},40] (* Harvey P. Dale, Aug 01 2021 *)
  • PARI
    Vec((2 + x + x^2) / (1 + x + 5*x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Dec 27 2017

Formula

G.f.: ( 2+x+x^2 ) / ( 1+x+5*x^2-x^3+x^4 ). - R. J. Mathar, Jun 18 2014
a(n) = -a(n-1) - 5*a(n-2) + a(n-3) - a(n-4) for n>3. - Colin Barker, Dec 27 2017
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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