A255162 Rational part of circle radii in nested circles and hexagons (see comment).

2, 0, 24, -288, 3744, -48384, 625536, -8087040, 104550912, -1351655424, 17474476032, -225913577472, 2920656642048, -37758842634240, 488153991315456, -6310954007396352, 81589295984541696, -1054802999903256576, 13636707550653579264

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: A109582 A375609 A308506 * A359006 A097563 A360643

Adjacent sequences: A255159 A255160 A255161 * A255163 A255164 A255165

Keyword

sign

Author

Kival Ngaokrajang, Feb 15 2015

Status

approved