Search: id:A022086
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%I A022086
%S A022086 0,3,3,6,9,15,24,39,63,102,165,267,432,699,1131,1830,2961,
%T A022086 4791,7752,12543,20295,32838,53133,85971,139104,225075,
%U A022086 364179,589254,953433,1542687,2496120,4038807,6534927,10573734
%N A022086 Fibonacci sequence beginning 0 3.
%D A022086 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, id. 7,17.
%H A022086 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A022086 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A022086 a(n) = round( (6phi-3)/5 phi^n ) (works for n>2) - Thomas Baruchel, Sep 
               08 2004
%F A022086 3*F(n). For n>1, F(n-2) + F(n+2), with F(n) = A000045(n).
%F A022086 a(n) = A119457(n+1,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 20 2006
%F A022086 First differences of A111314. - Ross La Haye (rlahaye(AT)new.rr.com), 
               May 31 2006
%F A022086 G.f.: 3x/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2008]
%p A022086 BB := n->if n=0 then 3; > elif n=1 then 0; > else BB(n-2)+BB(n-1); > 
               fi: > L:=[]: for k from 1 to 34 do L:=[op(L),BB(k)]: od: L; - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
%p A022086 with (combinat):seq(sum((fibonacci(n,1)),m=1..3),n=0..32); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
%t A022086 a={};b=0;c=3;AppendTo[a,b];AppendTo[a,c];Do[b=b+c;AppendTo[a,b];c=b+c;
               AppendTo[a,c],{n,1,9,1}];a (Vladimir Orlovsky, Jul 22 2008)
%Y A022086 Essentially the same as A097135. Cf. A026390, A036999.
%Y A022086 Sequence in context: A058628 A035528 A050337 this_sequence A097135 A167786 
               A167787
%Y A022086 Adjacent sequences: A022083 A022084 A022085 this_sequence A022087 A022088 
               A022089
%K A022086 nonn
%O A022086 0,2
%A A022086 N. J. A. Sloane (njas(AT)research.att.com).

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