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.

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A085005 A Von Koch curve related to the Golden ratio.

Original entry on oeis.org

1, 3, 4, 4, 3, 3, 4, 4, 3, 1, 0, 0, 1, 1, 0, 0, 1, 3, 4, 4, 5, 7, 10, 12, 13, 13, 14, 16, 17, 17, 16, 16, 17, 19, 20, 20, 21, 23, 26, 28, 29, 31, 34, 38, 41, 43, 44, 46, 49, 51, 52, 52, 53, 55, 56, 56, 55, 55, 56, 58, 59, 59, 60, 62, 65, 67, 68, 68, 69, 71, 72, 72, 71, 71, 72, 72, 71
Offset: 1

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Author

Benoit Cloitre, Jun 17 2003

Keywords

Links

Crossrefs

Cf. A083035, A083036, A083037, A083038, A085002, A085003, A085004.
Cf. A094200, A094201.

Programs

  • PARI
    a(n)=(-1)*sum(i=1,n,sum(j=1,i,(-1)^floor(j*(1+sqrt(5))/2)))

Formula

a(n)=(-1)*sum(i=1, n, sum(j=1, i, (-1)^floor(j*(1+sqrt(5))/2)))
a(n) = 2*sum(k = 1, n, sum(i = 1, k, b(i)))-n*(n+1)/2, where b(k) = floor(phi*k)-2*floor(phi*k/2)

A094201 a(n) = 4*n^5 + 10*n^4 + 13*n^3 + 11*n^2 + 5*n + 1.

Original entry on oeis.org

1, 44, 447, 2248, 7685, 20676, 47299, 96272, 179433, 312220, 514151, 809304, 1226797, 1801268, 2573355, 3590176, 4905809, 6581772, 8687503, 11300840, 14508501, 18406564, 23100947, 28707888, 35354425, 43178876, 52331319
Offset: 0

Views

Author

Benoit Cloitre, May 25 2004

Keywords

Comments

Let x(n) = (1/2)*(-(2*n+1) + sqrt((2*n+1)^2 + 4)) and f(k) = (-1)*(Sum_{i=1..k} Sum_{j=1..i} (-1)^floor(j*x(n))), then a(n) = Max{f(k): 0 < k < A094200(n)}.

Links

Crossrefs

Cf. A085005, A094200.

Programs

  • Mathematica
    LinearRecurrence[{6,-15,20,-15,6,-1},{1,44,447,2248,7685,20676},30] (* Harvey P. Dale, Oct 23 2021 *)
  • PARI
    a(n)=4*n^5+10*n^4+13*n^3+11*n^2+5*n+1

Formula

G.f.: (37*x^4 + 206*x^3 + 198*x^2 + 38*x + 1)/(x - 1)^6. - Jinyuan Wang, Apr 06 2020

Extensions

Corrected by T. D. Noe, Nov 09 2006
Showing 1-2 of 2 results.

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

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