The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A255162

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A255162

Rational part of circle radii in nested circles and hexagons (see comment).
(history; published version)

#17 by N. J. A. Sloane at Sun Feb 22 23:35:53 EST 2015

STATUS

editing

approved

#16 by N. J. A. Sloane at Sun Feb 22 23:34:44 EST 2015

NAME

a(n) is the rational Rational part of circle radii in nested circles and hexagons (see comment).

STATUS

proposed

editing

Discussion

Sun Feb 22

23:35

N. J. A. Sloane: I changed the definition. The reason is that a(n) is singular (one number) but "radii" is plural (many numbers).  Is this OK?

#15 by Jon E. Schoenfield at Mon Feb 16 12:48:28 EST 2015

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Mon Feb 16 12:48:26 EST 2015

COMMENTS

Inspired by Vitruvian Man But , but using hexagons instead of squares, starting with a hexagon whose sides are of length 4 (in some units). The radius of the circle is an integer in the real quadratic number field Q(sqrt(3)), namely R(n) = A(n) + B(n)*sqrt(3) with A(0)=2, A(n) = a(n), and B(0) = 1, B(n) = A255163(n). See illustrations in the links.

FORMULA

a(n) = -12*a(n-1) + 12*a(n-2).

G.f.: -2*(12*x+1) / (12*x^2 - 12*x - 1).

STATUS

proposed

editing

#13 by Kival Ngaokrajang at Mon Feb 16 05:25:21 EST 2015

STATUS

editing

proposed

#12 by Kival Ngaokrajang at Mon Feb 16 05:14:34 EST 2015

NAME

a(n) is the rational part of circle radii in nest nested circles and hexagons (see comment).

COMMENTS

Inspired by Vitruvian Man But using hexagons instead of squares. Starting , starting with a hexagon whose sides are of length of a hexagon equal to 4 (in some unit lengthunits). The radius of circle is an integer in the real quadratic number field Q(sqrt(3)), namely R(n) = A(n) + B(n)*sqrt(3) with A(0)=2, A(n) = a(n), and B(0) = 1, B(n) = A255163(n). See illustrations in the links.

STATUS

proposed

editing

Discussion

Mon Feb 16

05:25

Kival Ngaokrajang: Edited as Jon,s suggestion in A170931.

#11 by Colin Barker at Sun Feb 15 12:18:26 EST 2015

STATUS

editing

proposed

#10 by Colin Barker at Sun Feb 15 12:17:42 EST 2015

FORMULA

Conjectures from Colin Barker, Feb 15 2015: (Start)

a(n) = -12*a(n-1)+12*a(n-2).

G.f.: -2*(12*x+1) / (12*x^2-12*x-1).

(End)

STATUS

proposed

editing

#9 by Kival Ngaokrajang at Sun Feb 15 12:03:47 EST 2015

STATUS

editing

proposed

#8 by Kival Ngaokrajang at Sun Feb 15 11:55:46 EST 2015

LINKS

Kival Ngaokrajang, <a href="/A255162/a255162_2.pdf">Illustration of initial terms</a>, <a href="/A255162/a255162_1.pdf">Vitruvian Man</a>

Kival Ngaokrajang, <a href="/A255162/a255162_2.pdf">TITLE FOR LINK</a>