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 1-5 of 5 results.

A271950 Somos's sequence {b(5,n)} defined in comment in A078495: a(0)=a(1)=...=a(12)=1; for n>=13, a(n)=(a(n-1)*a(n-12)+a(n-6)*a(n-7))/a(n-13).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 15, 27, 47, 77, 119, 301, 519, 827, 1351, 2345, 4263, 10598, 35021, 91652, 200923, 396578, 742721, 2258305, 5126953, 14354017, 45716169, 138331649, 377080865, 1330892225, 5490413305, 16470110241
Offset: 0

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

Keywords

Links

Crossrefs

Cf. A006721, A078495, A268199, A271948, A271949.

Programs

  • Magma
    [n le 13 select 1 else ((Self(n-1)*Self(n-12) + Self(n-6)*Self(n- 7) )/Self(n-13)): n in [1..40]]; // G. C. Greubel, Feb 21 2018
  • Mathematica
    a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[5,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]== a[8]== a[9]== a[10]== a[11] ==a[12]==1,a[n]==(a[n-1]a[n-12]+a[n-6]a[n-7])/a[n-13]},a,{n,50}] (* Harvey P. Dale, May 01 2018 *)
  • PARI
    {a(n) = if(n< 12, 1, (a(n-1)*a(n-12) + a(n-6)*a(n-7))/a(n-13))};
for(n=0,40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

A271952 Somos's sequence {b(6,n)} defined in comment in A078495: a(0)=a(1)=...=a(14)=1; for n>=15, a(n)=(a(n-1)*a(n-14)+a(n-7)*a(n-8))/a(n-15).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 16, 28, 48, 78, 120, 176, 432, 728, 1120, 1736, 2832, 4864, 8576, 20224, 63808, 162624, 348224, 668288, 1204736, 2114560, 6175744, 13394432, 34860544, 104595968, 304683008, 807587840
Offset: 0

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

Keywords

Links

Crossrefs

Cf. A006721, A078495, A268199, A271948, A271949, A271950.

Programs

  • Magma
    [n le 15 select 1 else (Self(n-1)*Self(n-14)+Self(n-7)*Self(n-8))/Self(n-15): n in [1..60]]; // G. C. Greubel, Jul 30 2018
  • Mathematica
    a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[6,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
  • PARI
    {a(n) = if(n<= 15, 1, (a(n-1)*a(n-14) + a(n-7)*a(n-8))/a(n-15))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A271954 Somos's sequence {b(7,n)} defined in comment in A078495: a(0)=a(1)=...=a(16)=1; for n>=17, a(n)=(a(n-1)*a(n-16)+a(n-8)*a(n-9))/a(n-17).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 17, 29, 49, 79, 121, 177, 249, 597, 989, 1483, 2209, 3425, 5589, 9447, 16137, 36240, 109683, 273382, 574885, 1081260, 1898415, 3213378, 5381793, 15251949, 31924773, 78189885
Offset: 0

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

Keywords

Links

Crossrefs

Cf. A006721, A078495, A268199, A271948, A271949, A271950, A271952.

Programs

  • Magma
    [n le 17 select 1 else (Self(n-1)*Self(n-16)+Self(n-8)*Self(n-9))/Self(n-17): n in [1..60]]; // G. C. Greubel, Jul 30 2018
  • Mathematica
    a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[7,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
  • PARI
    {a(n) = if(n<= 17, 1, (a(n-1)*a(n-16) + a(n-8)*a(n-9))/a(n-17))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A271955 Somos's sequence {b(8,n)} defined in comment in A078495: a(0)=a(1)=...=a(18)=1; for n>=19, a(n)=(a(n-1)*a(n-18)+a(n-9)*a(n-10))/a(n-19).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 30, 50, 80, 122, 178, 250, 340, 800, 1308, 1924, 2780, 4136, 6452, 10476, 17348, 28720, 61664, 179696, 439304, 910464, 1686704, 2905792, 4793624, 7753616, 12537856
Offset: 0

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

Keywords

Links

Crossrefs

Cf. A006721, A078495, A268199, A271948, A271949, A271950, A271952, A271954.

Programs

  • Magma
    [n le 19 select 1 else (Self(n-1)*Self(n-18)+Self(n-9)*Self(n-10))/Self(n-19): n in [1..60]]; // G. C. Greubel, Jul 30 2018
  • Mathematica
    a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[8,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
  • PARI
    {a(n) = if(n<= 19, 1, (a(n-1)*a(n-18) + a(n-9)*a(n-10))/a(n-19))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A272038 Somos's sequence {b(9,n)} defined in comment in A078495: a(0)=a(1)=...=a(20)=1; for n>=21, a(n)=(a(n-1)*a(n-20)+a(n-10)*a(n-11))/a(n-21).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 31, 51, 81, 123, 179, 251, 341, 451, 1045, 1691, 2451, 3459, 4977, 7467, 11679, 18755, 30349, 48763, 100474, 282777, 679512, 1391391, 2547414, 4327101
Offset: 0

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 18 2016

Keywords

Links

Crossrefs

Cf. A006721, A078495, A268199, A271954, A271948, A271949, A271950, A271952, A271955.

Programs

  • Ruby
    def b(k, n)
  b = Array.new(2 * k + 3, 1)
  (2 * k + 3..n).each{|i|
    j = (b[i - 1] * b[i - 2 * k - 2] + b[i - k - 1] * b[i - k - 2]) / b[i - 2 * k - 3].to_r
    j = j.to_i if j.denominator == 1
    b[i] = j
  }
  b[0..n]
end
p b(9, n) # Seiichi Manyama, May 04 2016
Showing 1-5 of 5 results.

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