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A027674 Numerical distance between m-th and (m+n)-th spheres in loxodromic sequence of spheres in which each 5 consecutive spheres are in mutual contact. 2
-1, 1, 1, 1, 1, 5, 7, 13, 25, 49, 89, 169, 319, 601, 1129, 2129, 4009, 7549, 14215, 26773, 50417, 94945, 178801, 336721, 634111, 1194161, 2248849, 4235041, 7975441, 15019381, 28284551, 53265565, 100309897, 188903953 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Sequence in context: A191022 A262958 A155757 * A124307 A158294 A090610

Adjacent sequences:  A027671 A027672 A027673 * A027675 A027676 A027677

KEYWORD

sign,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)