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A027674
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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.
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2
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-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; internal format)
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OFFSET
| 0,6
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REFERENCES
| H. S. M. Coxeter, 5 spheres in mutual contact, Abstracts AMS 18 (1997), p. 431, #924-05-202; also Math. Intell. 19(4) 1997 pp. 41-47.
H. S. M. Coxeter, 1998, Numerical distances among the circles in a loxodromic sequence, Nieuw Arch. Wisk, 16, pp. 1-9.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-1)-a(n-5).
7a(n) = (-1)^(n+1)*2 + 3*Sum{v=0 to [ 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 (fvlamoen(AT)hotmail.com) ].
G.f.:(-1-x^4+x^2+2*x)/((x+1)*(x^4-2*x^3+x^2-2*x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
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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;
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MATHEMATICA
| CoefficientList[ Series[ (-1+2x+x^2-x^4) / (1-x-x^2-x^3-x^4+x^5), {x, 0, 33}], x] (* From Jean-François Alcover, Nov 29 2011, after Maksym Voznyy *)
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CROSSREFS
| Sequence in context: A078724 A191022 A155757 * A124307 A158294 A090610
Adjacent sequences: A027671 A027672 A027673 * A027675 A027676 A027677
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KEYWORD
| sign,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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