Search: id:A027674
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%I A027674
%S A027674 1,1,1,1,1,5,7,13,25,49,89,169,319,601,1129,2129,4009,7549,
%T A027674 14215,26773,50417,94945,178801,336721,634111,1194161,2248849,
%U A027674 4235041,7975441,15019381,28284551,53265565,100309897,188903953
%V A027674 -1,1,1,1,1,5,7,13,25,49,89,169,319,601,1129,2129,4009,7549,
%W A027674 14215,26773,50417,94945,178801,336721,634111,1194161,2248849,
%X A027674 4235041,7975441,15019381,28284551,53265565,100309897,188903953
%N 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.
%D A027674 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.
%D A027674 H. S. M. Coxeter, 1998, Numerical distances among the circles in a loxodromic 
               sequence, Nieuw Arch. Wisk, 16, pp. 1-9.
%F A027674 a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-1)-a(n-5).
%F A027674 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) ].
%F A027674 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]
%p A027674 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;
%Y A027674 Sequence in context: A155006 A078724 A155757 this_sequence A124307 A158294 
               A090610
%Y A027674 Adjacent sequences: A027671 A027672 A027673 this_sequence A027675 A027676 
               A027677
%K A027674 sign,nice
%O A027674 0,6
%A A027674 N. J. A. Sloane (njas(AT)research.att.com).

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