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 1-6 of 6 results.

A271800 Five steps forward, four steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10
Offset: 0

Views

Author

Wesley Ivan Hurt, Apr 15 2016

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).

Programs

  • Maple
    A271800:=n->add((-1)^floor((2*i-2)/9), i=1..n): seq(A271800(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/9], {i, n}], {n, 0, 100}]
  • PARI
    concat(0, Vec(x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8)/((1-x)^2*(1+x+x^2)*(1+x^3+x^6)) + O(x^50))) \\ Colin Barker, Apr 15 2016

Formula

a(n) = a(n-1) + a(n-9) - a(n-10) for n>9.
a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/9).
G.f.: x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8) / ((1-x)^2*(1+x+x^2)*(1+x^3+x^6)). - Colin Barker, Apr 15 2016

A271859 Six steps forward, five steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 8, 9, 10, 11
Offset: 0

Views

Author

Wesley Ivan Hurt, Apr 15 2016

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).
Cf. A271800 (five steps forward, four steps back).

Programs

  • Maple
    A271859:=n->add((-1)^floor((2*i-2)/11), i=1..n): seq(A271859(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/11], {i, n}], {n, 0, 100}]
  • PARI
    concat(0, Vec(x*(1+x+x^2+x^3+x^4+x^5-x^6-x^7-x^8-x^9-x^10) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)) + O(x^50))) \\ Colin Barker, Apr 16 2016

Formula

a(n) = a(n-1) + a(n-11) - a(n-12) for n>11.
a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/11).
G.f.: x*(1+x+x^2+x^3+x^4+x^5-x^6-x^7-x^8-x^9-x^10) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)). - Colin Barker, Apr 16 2016

A287655 Seven steps forward, six steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10
Offset: 0

Views

Author

Wesley Ivan Hurt, May 29 2017

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).
Cf. A271800 (five steps forward, four steps back).
Cf. A271859 (six steps forward, five steps back).

Programs

  • Maple
    A287655:=n->add((-1)^floor((2*i-2)/13), i=1..n): seq(A287655(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/13], {i, n}], {n, 0, 100}]

Formula

a(n) = a(n-1) + a(n-13) - a(n-14) for n > 13.
a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/13).

A287793 Eight steps forward, seven steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11
Offset: 0

Views

Author

Wesley Ivan Hurt, May 31 2017

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).
Cf. A271800 (five steps forward, four steps back).
Cf. A271859 (six steps forward, five steps back).
Cf. A287655 (seven steps forward, six steps back).

Programs

  • Maple
    A287793:=n->add((-1)^floor((2*i-2)/15), i=1..n): seq(A287793(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/15], {i, n}], {n, 0, 100}]

Formula

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/15).
a(n) = a(n-1) + a(n-15) - a(n-16) for n > 15.

A287794 Nine steps forward, eight steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10
Offset: 0

Views

Author

Wesley Ivan Hurt, May 31 2017

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).
Cf. A271800 (five steps forward, four steps back).
Cf. A271859 (six steps forward, five steps back).
Cf. A287655 (seven steps forward, six steps back).
Cf. A287793 (eight steps forward, seven steps back).

Programs

  • Maple
    a:=n->add((-1)^floor((2*i-2)/17), i=1..n): seq(a(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/17], {i, n}], {n, 0, 100}]
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1},100] (* Harvey P. Dale, Aug 25 2024 *)

Formula

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/17).
a(n) = a(n-1) + a(n-17) - a(n-18) for n > 17.

A287796 Ten steps forward, nine steps back.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8
Offset: 0

Views

Author

Wesley Ivan Hurt, May 31 2017

Keywords

Links

Crossrefs

Cf. A008611 (one step back, two steps forward).
Cf. A058207 (three steps forward, two steps back).
Cf. A260644 (four steps forward, three steps back).
Cf. A271800 (five steps forward, four steps back).
Cf. A271859 (six steps forward, five steps back).
Cf. A287655 (seven steps forward, six steps back).
Cf. A287793 (eight steps forward, seven steps back).
Cf. A287794 (nine steps forward, eight steps back).

Programs

  • Maple
    A287796:=n->add((-1)^floor((2*i-2)/19), i=1..n): seq(A287796(n), n=0..200);
  • Mathematica
    Table[Sum[(-1)^Floor[(2 i - 2)/19], {i, n}], {n, 0, 100}]

Formula

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/19).
a(n) = a(n-1) + a(n-19) - a(n-20) for n > 19.
Showing 1-6 of 6 results.

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