OFFSET
0,6
REFERENCES
H. S. M. Coxeter, 5 spheres in mutual contact, Abstracts AMS 18 (1997), p. 431, #924-05-202.
H. S. M. Coxeter, 1998, Numerical distances among the circles in a loxodromic sequence, Nieuw Arch. Wisk, 16, pp. 1-9.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
H. S. M. Coxeter, Numerical distances among the spheres in a loxodromic sequence, Math. Intell. 19(4) 1997 pp. 41-47. See page 41.
Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, -1).
FORMULA
a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5). - corrected by Harvey P. Dale, Apr 12 2013
7a(n) = (-1)^(n+1)*2 + 3*Sum_{v=0..floor(n/2}} * (n/(n-v)) * binomial(n-v, v)*u(n-2v) where u(n) = 2u(n-1) + u(n-2) and u(0)=-1, u(1)=2. - Floor van Lamoen
G.f.:(-1-x^4+x^2+2*x)/((x+1)*(x^4-2*x^3+x^2-2*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
MAPLE
f := proc(n) option remember; if n=0 then -1 elif n=1 then 1 elif n=2 then 1 elif n=3 then 1 elif n=4 then 1 else f(n-1)+f(n-2)+f(n-3)+f(n-4)-f(n-5); fi; end;
MATHEMATICA
CoefficientList[ Series[ (-1+2x+x^2-x^4) / (1-x-x^2-x^3-x^4+x^5), {x, 0, 33}], x] (* Jean-François Alcover, Nov 29 2011, after Maksym Voznyy *)
LinearRecurrence[{1, 1, 1, 1, -1}, {-1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Apr 12 2013 *)
PROG
(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 1, 1, 1, 1]^n*[-1; 1; 1; 1; 1])[1, 1] \\ Charles R Greathouse IV, Jun 16 2015
CROSSREFS
KEYWORD
sign,nice,easy
AUTHOR
STATUS
approved