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A092550 Expansion of -x*(1+x+x^2+x^4)/(-1+2*x^3+x^6).

%I A092550 #31 Jun 13 2015 00:51:18
%S A092550 1,1,1,2,3,2,5,7,5,12,17,12,29,41,29,70,99,70,169,239,169,408,577,408,
%T A092550 985,1393,985,2378,3363,2378,5741,8119,5741,13860,19601,13860,33461,
%U A092550 47321,33461,80782,114243,80782,195025,275807,195025,470832,665857
%N A092550 Expansion of -x*(1+x+x^2+x^4)/(-1+2*x^3+x^6).
%C A092550 If prefaced with a 1: denominators in convergents to barover:[1, 0, 1] as follows:
%C A092550 1,....0,....1,....1,....0,....1,....1,....0,....1,....
%C A092550 1/1,..0/1,..1/2,..1/3...1/2...2/5...3/7...2/5...5/12,...;
%C A092550 _Gary W. Adamson_, Mar 25 2014
%C A092550 For k(n), a term in A249576, k(n+6) mod (k(n+5)) = a(n). - _Russell Walsmith_, Nov 27 2014
%H A092550 Marcia Edson, Scott Lewis and Omer Yayenie, <a href="http://www.emis.de/journals/INTEGERS/papers/l32/l32.Abstract.html">The k-periodic Fibonacci sequence and an extended Binet's formula</a>, INTEGERS 11 (2011) #A32.
%H A092550 D. Panario, M. Sahin, Q. Wang, <a href="http://www.emis.de/journals/INTEGERS/papers/n78/n78.Abstract.html">A family of Fibonacci-like conditional sequences</a>, INTEGERS, Vol. 13, 2013, #A78.
%H A092550 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,1).
%F A092550 a(n) = a(n-2) if 3|n, otherwise a(n)= a(n-1)+a(n-2).
%F A092550 From _R. J. Mathar_, Dec 08 2010: (Start)
%F A092550 a(n)= +2*a(n-3) +a(n-6).
%F A092550 G.f.: -x*(1+x+x^2+x^4)/(-1+2*x^3+x^6).
%F A092550 a(3n+1) = A000129(n+1). a(3n)=A000129(n). a(3n+2)= A078057(n). (End)
%t A092550 m=3 fib[n_Integer?Positive] :=fib[n] =If[Mod[n, m]==0, fib[n-2], fib[n-1]+fib[n-2]] fib[0]=fib[1] = fib[2] = 1 digits=50 a=Table[fib[n], {n, 1, digits}]
%t A092550 LinearRecurrence[{0,0,2,0,0,1},{1,1,1,2,3,2},50] (* _Harvey P. Dale_, Jan 13 2015 *)
%Y A092550 Cf. A000045.
%K A092550 nonn
%O A092550 1,4
%A A092550 _Roger L. Bagula_, Apr 08 2004
%E A092550 Edited, and new name, _Joerg Arndt_, Sep 17 2013