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.

User: Kyle MacLean Smith

Kyle MacLean Smith's wiki page.

Kyle MacLean Smith has authored 4 sequences.

A330390 G.f.: (1 + 15*x) / (1 - 2*x - 17*x^2).

Original entry on oeis.org

1, 17, 51, 391, 1649, 9945, 47923, 264911, 1344513, 7192513, 37241747, 196756215, 1026622129, 5398099913, 28248776019, 148265250559, 776759693441, 4074028646385, 21352972081267, 111964431151079, 586929387683697, 3077254104935737, 16132307800494323
Offset: 0

Views

Author

Kyle MacLean Smith, Dec 13 2019

Keywords

Links

Crossrefs

Cf. A164544, A328606.

Programs

  • Mathematica
    CoefficientList[Series[(1+15x)/(1-2x-17x^2),{x,0,30}],x] (* or *) LinearRecurrence[{2,17},{1,17},30] (* Harvey P. Dale, Jul 31 2021 *)
  • PARI
    Vec((1 + 15*x) / (1 - 2*x - 17*x^2) + O(x^25)) \\ Colin Barker, Jan 25 2020

Formula

a(n) = 2*a(n-1) + 17*a(n-2) for n>1.
a(n)/a(n-1) ~ 1 + 3*sqrt(2).
a(n) = ((1 - 3*sqrt(2))^n*(-16+3*sqrt(2)) + (1+3*sqrt(2))^n*(16 + 3*sqrt(2))) / (6*sqrt(2)). - Colin Barker, Dec 14 2019

A328605 Expansion of (1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4).

Original entry on oeis.org

1, 5, 10, 45, 95, 415, 890, 3855, 8305, 35885, 77410, 334245, 721295, 3113815, 6720290, 29009655, 62611105, 270270485, 583326010, 2518004445, 5434634495, 23459291215, 50632463690, 218561383455, 471723701905, 2036254321085, 4394872830610, 18971017266645, 40945381419695
Offset: 0

Views

Author

Kyle MacLean Smith, Oct 20 2019

Keywords

Links

Crossrefs

Cf. A328604, A328606.

Programs

  • Mathematica
    CoefficientList[Series[(1+5x-2x^2-15x^3)/(1-12x^2+25x^4),{x,0,30}],x] (* or *) LinearRecurrence[ {0,12,0,-25},{1,5,10,45},30] (* Harvey P. Dale, Jul 02 2024 *)
  • PARI
    Vec((1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4) + O(x^30)) \\ Colin Barker, Dec 13 2019

Formula

a(n) = 12*a(n-2) - 25*a(n-4) for n>3. - Colin Barker, Oct 21 2019
a(2*n)/a(2*n-1) ~ 2*a(2*n+1)/a(2*n) ~ 1 + sqrt(11).

A328606 Expansion of (1 + 9*x) / (1 - 2*x - 11*x^2).

Original entry on oeis.org

1, 11, 33, 187, 737, 3531, 15169, 69179, 305217, 1371403, 6100193, 27285819, 121673761, 543491531, 2425394433, 10829195707, 48337730177, 215796613131, 963308258209, 4300379260859, 19197149362017, 85698470593483, 382565584169153, 1707814344866619, 7623850115593921, 34033658024720651
Offset: 0

Views

Author

Kyle MacLean Smith, Oct 20 2019

Keywords

Links

Crossrefs

Cf. A328604, A328605.

Programs

  • PARI
    Vec((1 + 9*x) / (1 - 2*x - 11*x^2) + O(x^30)) \\ Colin Barker, Dec 13 2019

Formula

a(n) = 2*a(n-1) + 11*a(n-2) for n>1. - Colin Barker, Oct 21 2019
a(n)/a(n-1) ~ 1 + 2*sqrt(3).

A328604 G.f.: (1 + 7*x) / (1 - 2*x - 9*x^2).

Original entry on oeis.org

1, 9, 27, 135, 513, 2241, 9099, 38367, 158625, 662553, 2752731, 11468439, 47711457, 198638865, 826680843, 3441111471, 14322350529, 59614704297, 248130563355, 1032793465383, 4298762000961, 17892665190369, 74474188389387, 309982363492095, 1290232422488673, 5370306116406201
Offset: 0

Views

Author

Kyle MacLean Smith, Oct 20 2019

Keywords

Links

Programs

  • PARI
    Vec((1 + 7*x) / (1 - 2*x - 9*x^2) + O(x^30)) \\ Colin Barker, Dec 13 2019

Formula

a(n) = 2*a(n-1) + 9*a(n-2) for n>1. - Colin Barker, Oct 21 2019
a(n)/a(n-1) ~ 1 + sqrt(10).

Extensions

Edited by N. J. A. Sloane, Dec 05 2019

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

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