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.

A256569 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 6, 21, 61, 171, 461, 1181, 2951
Offset: 1

Views

Author

Kival Ngaokrajang, Apr 02 2015

Keywords

Comments

Inspired by A255870. But at the higher iterations, the perimeter would be an irregular polygon instead of a pentagon. The construction rule is vertex to vertex expansion. See illustration in the links.

Links

Crossrefs

Cf. A255870, A256429, A256571.

A256582 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 11, 46, 146, 416, 1136, 2776
Offset: 1

Views

Author

Kival Ngaokrajang, Apr 04 2015

Keywords

Comments

Inspired by A255870. But the scale factor is tan(3*Pi/10)/(1+phi) instead of 1/phi.
See illustration in the links.

Links

Crossrefs

Cf. A255870, A256429, A256569, A256571, A256583, A256597.

A256583 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 11, 66, 336, 1666, 8186
Offset: 1

Views

Author

Kival Ngaokrajang, Apr 04 2015

Keywords

Comments

Inspired by A255870. But the scale factor is (1/phi)^2 instead of 1/phi.
See illustration in the links.

Links

Crossrefs

Cf. A255870, A256429, A256569, A256571, A256582, A256597.

A256597 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 11, 76, 436, 2441
Offset: 1

Views

Author

Kival Ngaokrajang, Apr 04 2015

Keywords

Comments

Inspired by A255870. But the scale factor is tan(Pi/10) instead of 1/phi.
See illustration in the links.

Links

Crossrefs

Cf. A255870, A256429, A256569, A256571, A256582, A256583.

A263418 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 6, 21, 51, 106, 201, 361, 626, 1061, 1771, 2926, 4801, 7841, 12766, 20741, 33651, 54546, 88361, 143081, 231626, 374901, 606731, 981846, 1588801, 2570881, 4159926, 6731061, 10891251, 17622586, 28514121, 46137001, 74651426, 120788741, 195440491, 316229566
Offset: 0

Views

Author

Kival Ngaokrajang, Oct 17 2015

Keywords

Comments

Inspired by A255870.

Links

Crossrefs

Cf. A001911, A255870, A256429, A256569, A256571, A256582, A256583, A263419.

Programs

  • PARI
    {a=1; print1(a, ", "); for(n=1,100, b=fibonacci(n+3)-2; a=a+5*b; print1 (a, ", "))}
  • PARI
    Vec(-(x^3+5*x^2+3*x+1)/((x-1)^2*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Oct 18 2015

Formula

a(0) = 1, for n > 0, a(n) = a(n-1) + 5*(fibonacci(n+3)-2) or a(n) = a(n-1) + 5*A001911(n).
From Colin Barker, Oct 18 2015: (Start)
a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4) for n>3.
G.f.: -(x^3+5*x^2+3*x+1) / ((x-1)^2*(x^2+x-1)).
(End)
a(n) = -14 + 2^(-1-n)*((25-11*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) - 10*(1+n). - Colin Barker, Mar 12 2017

A263419 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

Original entry on oeis.org

1, 6, 11, 26, 51, 106, 201, 396, 751, 1446, 2741
Offset: 0

Views

Author

Kival Ngaokrajang, Oct 17 2015

Keywords

Comments

Inspired by A255870, also same as A263418 but overlaps are prohibited.

Links

Crossrefs

Cf. A255870, A256429, A256569, A256571, A256582, A256583, A263418.
Showing 1-6 of 6 results.

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