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A255162 Rational part of circle radii in nested circles and hexagons (see comment). 3
2, 0, 24, -288, 3744, -48384, 625536, -8087040, 104550912, -1351655424, 17474476032, -225913577472, 2920656642048, -37758842634240, 488153991315456, -6310954007396352, 81589295984541696, -1054802999903256576, 13636707550653579264 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Inspired by Vitruvian Man, 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.

LINKS

Table of n, a(n) for n=0..18.

Kival Ngaokrajang, Illustration of initial terms, Vitruvian Man

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)

PROG

(PARI){a=2; b=1; print1(a, ", "); for(n=1, 30, c=12*b-6*a; d=4*a-6*b; print1(c, ", "); a=c; b=d)}

CROSSREFS

Cf. A174968, A170931, A094013, A255163.

Sequence in context: A009799 A109582 A308506 * A097563 A158045 A157304

Adjacent sequences:  A255159 A255160 A255161 * A255163 A255164 A255165

KEYWORD

sign

AUTHOR

Kival Ngaokrajang, Feb 15 2015

STATUS

approved

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Last modified October 26 00:31 EDT 2021. Contains 348256 sequences. (Running on oeis4.)