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.

A108587 a(n) = floor(n/(1-sin(1))).

Original entry on oeis.org

6, 12, 18, 25, 31, 37, 44, 50, 56, 63, 69, 75, 82, 88, 94, 100, 107, 113, 119, 126, 132, 138, 145, 151, 157, 164, 170, 176, 182, 189, 195, 201, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 309, 315, 321, 328, 334, 340, 346
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2005

Keywords

Comments

Beatty sequence for 1/(1-sin(1)); complement of A108120.

Links

Crossrefs

Cf. A038130, A049469, A108120, A108593, A206530.

Programs

  • Magma
    [Floor(n/(1-Sin(1))): n in [1..60]]; // G. C. Greubel, Dec 19 2022
  • Mathematica
    Table[Floor[n/(1-Sin[1])], {n, 60}] (* G. C. Greubel, Dec 19 2022 *)
  • SageMath
    [int(n/(1-sin(1))) for n in range(1,61)] # G. C. Greubel, Dec 19 2022

A206307 a(n) = ((2*n+2)*(2*n+3) - 1)*a(n-1) + 2*n*(2*n+1)*a(n-2), a(0)=0, a(1)=6.

Original entry on oeis.org

0, 6, 246, 17718, 1948974, 304039950, 63848389494, 17366761942374, 5939432584291902, 2494561685402598846, 1262248212813715016070, 757348927688229009642006, 531658947237136764768688206, 431707065156555052992174823278
Offset: 0

Views

Author

Seiichi Kirikami, Feb 11 2012

Keywords

Comments

The numerators of the fractions limiting to the value of A206530.

References

  • E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Links

Crossrefs

Cf. A002943, A125202, A206308, A206530.

Programs

  • Magma
    [n le 2 select 6*(n-1) else (4*n^2+2*n-1)*Self(n-1) + 2*(n-1)*(2*n-1)*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 20 2022
  • Mathematica
    RecurrenceTable[{a[n]==((2n+3)(2n+2)-1)a[n-1]+2n(2n+1)a[n-2],a[0]==0,a[1]==6},a,{n,15}]
  • SageMath
    @CachedFunction
def a(n): return 6*n if (n<2) else (4*n^2+10*n+5)*a(n-1) + 2*n*(2*n+1)*a(n-2)
[a(n) for n in range(31)] # G. C. Greubel, Dec 20 2022

Formula

a(n) = A125202(n+2)*a(n-1) + A002943(n)*a(n-2), a(0) = 0, a(1) = 6.

A206308 a(n) = ((2*n+2)*(2*n+3) - 1)*a(n-1) + 2*n*(2*n+1)*a(n-2), a(0)=1, a(1)=19.

Original entry on oeis.org

1, 19, 799, 57527, 6327971, 987163475, 207304329751, 56386777692271, 19284277970756683, 8099396747717806859, 4098294754345210270655, 2458976852607126162392999, 1726201750530202565999885299, 1401675821430524483591906862787
Offset: 0

Views

Author

Seiichi Kirikami, Feb 11 2012

Keywords

Comments

The denominators of the fractions limiting to the value of A206530.

References

  • E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Links

Crossrefs

Cf. A002943, A125202, A206307, A206530.

Programs

  • Magma
    [n le 2 select 19^(n-1) else (4*n^2+2*n-1)*Self(n-1) + 2*(n-1)*(2*n-1)*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 21 2022
  • Mathematica
    RecurrenceTable[{a[n]==((2n+3)(2n+2)-1)a[n-1]+2n(2n+1)a[n-2], a[0]==1, a[1]==19}, a, {n,15}]
  • SageMath
    @CachedFunction # a = A206308
def a(n): return 19^n if (n<2) else (4*n^2+10*n+5)*a(n-1) + 2*n*(2*n+1)*a(n-2)
[a(n) for n in range(31)] # G. C. Greubel, Dec 21 2022

Formula

a(n) = A125202(n+2)*a(n-1) + A002943(n)*a(n-2), with a(0) = 1, a(1) = 19.
Showing 1-3 of 3 results.

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