OFFSET
0,1
COMMENTS
Sequence gives the rational part of the radii of the circles in nested circles and squares inspired by Vitruvian Man, starting with a square 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(2)), namely R(n) = A(n-1) + B(n)*sqrt(2) with A(-1)=1, for n >= 1, A(n-1) = A170931(n-1)*-1^(n-1); and B(n) = A094013(n)*-1^n. See illustrations in the links. - Kival Ngaokrajang, Feb 15 2015
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Kival Ngaokrajang, Illustration of initial terms, Vitruvian Man
Index entries for linear recurrences with constant coefficients, signature (4, 4).
FORMULA
From R. J. Mathar, Feb 05 2010: (Start)
a(n) = 2*A084128(n) = 4*a(n-1) + 4*a(n-2).
G.f.: 2*(1-2*x)/(1 - 4*x - 4*x^2). (End)
EXAMPLE
L(n,0)=2, L(n,1)=n.
MATHEMATICA
CoefficientList[Series[2 (1 - 2 x) / (1 - 4 x - 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 16 2015 *)
LinearRecurrence[{4, 4}, {2, 4}, 30] (* Harvey P. Dale, Sep 03 2016 *)
PROG
(PARI) x='x+O('x^30); Vec(2*(1-2*x)/(1 - 4*x - 4*x^2)) \\ G. C. Greubel, Dec 21 2017
(Magma) I:=[2, 4]; [n le 5 select I[n] else 4*Self(n-1)+4*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Claudio Peruzzi (claudio.peruzzi(AT)gmail.com), Feb 04 2010
STATUS
approved