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.

A017887 Expansion of 1/(1 - x^10 - x^11).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of compositions (ordered partitions) of n into parts 10 and 11. - Ilya Gutkovskiy, May 27 2017

Links

Crossrefs

Column k=10 of A306713.
Cf. A017886, A017888, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Programs

  • Magma
    m:=80; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11))); // Vincenzo Librandi, Jul 01 2013
  • Magma
    I:=[1,0,0,0,0,0,0,0,0,0,1]; [n le 11 select I[n] else Self(n-10)+Self(n-11): n in [1..80]]; // Vincenzo Librandi, Jul 01 2013
  • Mathematica
    CoefficientList[Series[1 / (1 - Total[x^Range[10, 11]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,0,0,1},100] (* Harvey P. Dale, Feb 04 2015 *)
  • SageMath
    def A017887_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^10-x^(11)) ).list()
A017887_list(100) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-10) + a(n-11) for n > 10. - Vincenzo Librandi, Jul 01 2013
a(n) = Sum_{k=0..floor(n/10)} binomial(k,n-10*k). - Seiichi Manyama, Oct 01 2024

A017888 Expansion of 1/(1 - x^10 - x^11 - x^12).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 1, 5, 15, 30, 45, 51, 45, 30, 15, 5, 2, 6, 21, 50, 90, 126, 141, 126, 90, 50
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of compositions (ordered partitions) of n into parts 10, 11 and 12. - Ilya Gutkovskiy, May 27 2017

Links

Crossrefs

Cf. A017887, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Programs

  • Magma
    m:=80; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^10-x^11-x^12))); // Vincenzo Librandi, Jul 01 2013
  • Mathematica
    CoefficientList[Series[1 / (1 - Total[x^Range[10, 12]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
  • PARI
    my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12)) \\ Altug Alkan, Oct 04 2018
  • SageMath
    def A017888_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^(13)) ).list()
A017888_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-10) + a(n-11) + a(n-12), for n > 11. - Vincenzo Librandi, Jul 01 2013

A017889 Expansion of 1/(1-x^10-x^11-x^12-x^13).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 0, 1, 3, 6, 10, 12, 12, 10, 6, 3, 1, 1, 4, 10, 20, 31, 40, 44, 40, 31, 20, 11, 9, 16, 35, 65, 101, 135, 155, 155, 135, 102, 71, 56, 71, 125
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12 and 13. - Ilya Gutkovskiy, May 27 2017

Links

Crossrefs

Cf. A017887, A017888, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

Programs

  • Magma
    m:=80; R:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^10-x^11-x^12-x^13))); // Vincenzo Librandi, Jul 01 2013
  • Mathematica
    CoefficientList[Series[1 / (1 - Total[x^Range[10, 13]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
  • SageMath
    def A017889_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^(14)) ).list()
A017889_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jul 01 2013
Showing 1-3 of 3 results.

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

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