login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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.
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
KEYWORD
sign
AUTHOR
Kival Ngaokrajang, Feb 15 2015
STATUS
approved