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 1-4 of 4 results.

A251707 6-step Fibonacci sequence starting with (0,0,0,1,0,0).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 1, 2, 4, 8, 15, 30, 60, 119, 236, 468, 928, 1841, 3652, 7244, 14369, 28502, 56536, 112144, 222447, 441242, 875240, 1736111, 3443720, 6830904, 13549664, 26876881, 53312520, 105749800, 209763489, 416083258, 825335612, 1637121560, 3247366239
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 6-step Fibonacci sequences are A001592, A074584, A251706, A251708, A251709.

Programs

  • Mathematica
    LinearRecurrence[Table[1, {6}], {0, 0, 0, 1, 0, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+6) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5).
G.f.: x^3*(-1+x+x^2)/(-1+x+x^2+x^3+x^4+x^5+x^6) . - R. J. Mathar, Feb 27 2023

A251706 6-step Fibonacci sequence starting with (0,0,0,0,1,0).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 31, 62, 123, 244, 484, 960, 1904, 3777, 7492, 14861, 29478, 58472, 115984, 230064, 456351, 905210, 1795559, 3561640, 7064808, 14013632, 27797200, 55138049, 109370888, 216946217, 430330794, 853596780, 1693179928, 3358562656
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Comments

a(n+6) equals the number of n-length binary words avoiding runs of zeros of lengths 6i+5, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

Links

Crossrefs

Other 6-step Fibonacci sequences are A001592, A074584, A251707, A251708, A251709.

Programs

  • Mathematica
    LinearRecurrence[Table[1, {6}], {0, 0, 0, 0, 1, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+6) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5).
G.f.: x^4*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6) . - R. J. Mathar, Mar 28 2025
a(n) = A001592(n+1)-A001592(n). - R. J. Mathar, Mar 28 2025

A251709 6-step Fibonacci sequence starting with (0,1,0,0,0,0).

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 1, 2, 3, 6, 12, 24, 48, 95, 188, 373, 740, 1468, 2912, 5776, 11457, 22726, 45079, 89418, 177368, 351824, 697872, 1384287, 2745848, 5446617, 10803816, 21430264, 42508704, 84319536, 167254785, 331763722, 658080827, 1305357838, 2589285412
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 6-step Fibonacci sequences are A001592, A074584, A251706, A251707, A251708.

Programs

  • Mathematica
    LinearRecurrence[Table[1, {6}], {0, 1, 0, 0, 0, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+6) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5).
G.f.: x*(-1+x+x^2+x^3+x^4)/(-1+x+x^2+x^3+x^4+x^5+x^6) . - R. J. Mathar, Feb 27 2023

A382479 Number of palindromic binary strings of length n having no 6-runs of 1's.

Original entry on oeis.org

1, 2, 2, 4, 4, 8, 7, 15, 14, 30, 28, 60, 56, 119, 111, 236, 220, 468, 436, 928, 865, 1841, 1716, 3652, 3404, 7244, 6752, 14369, 13393, 28502, 26566, 56536, 52696, 112144, 104527, 222447, 207338, 441242, 411272, 875240, 815792, 1736111, 1618191, 3443720, 3209816, 6830904, 6366936
Offset: 0

Views

Author

R. J. Mathar, Mar 28 2025

Keywords

Links

Crossrefs

Cf. A251707 (bisection), A251708 (bisection).
Cf. A123231 (2-runs), A001590 (3-runs), A382478 (4-runs), A251653 (5-runs).

Programs

  • Magma
    m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(-(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12))); // Vincenzo Librandi, May 20 2025
  • Mathematica
    LinearRecurrence[{0,1,0,1,0,1,0,1,0,1,0,1},{1,2,2,4,4,8,7,15,14,30,28,60},50] (* Vincenzo Librandi, May 20 2025 *)

Formula

G.f.: -(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12).
Showing 1-4 of 4 results.

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