%I A078343
%S A078343 1,2,3,8,19,46,111,268,647,1562,3771,9104,21979,53062,128103,309268,746639,
%T A078343 1802546,4351731,10506008,25363747,61233502,147830751,356895004,861620759,
%U A078343 2080136522,5021893803,12123924128,29269742059,70663408246,170596558551
%V A078343 -1,2,3,8,19,46,111,268,647,1562,3771,9104,21979,53062,128103,309268,746639,
%W A078343 1802546,4351731,10506008,25363747,61233502,147830751,356895004,861620759,
%X A078343 2080136522,5021893803,12123924128,29269742059,70663408246,170596558551
%N A078343 a(0) = -1, a(1) = 2; a(n) = 2*a(n-1) + a(n-2).
%D A078343 H. S. M. Coxeter, 1998, Numerical distances among the circles in a loxodromic 
               sequence, Nieuw Arch. Wisk, 16, pp. 1-9.
%H A078343 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A078343 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A078343 For the unsigned version: a(1)=1; a(2)=2; a(n) = sum(k=2, n-1, a(k) + 
               a(k-1) ).
%F A078343 a(n) is asymptotic to (1/4)*(8-5*sqrt(2))*(1+sqrt(2))^n.
%F A078343 a(n) = A048746(n-3) + 2, for n>2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Oct 17 2003
%F A078343 a(n)=2Pell(n)-Pell(n-1); abs(A078343(n))=2*0^n+2Pell(n)-Pell(n-1); abs(A078343(n))=sum{k=0..floor(n/
               2), (C(n-k-1, k)-C(n-k-1, k-1))2^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), 
               Dec 23 2004
%F A078343 O.g.f.: (1-4*x)/(-1+2*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 15 2008
%F A078343 a(n)=first binomial transform of 2,1,4,2,8... [From Al Hakanson (hawkuu(AT)gmail.com), 
               Jun 22 2009]
%p A078343 f:=proc(n) option remember; if n=0 then RETURN(-1); fi; if n=1 then RETURN(2); 
               fi; 2*f(n-1)+f(n-2); end;
%t A078343 a=2;b=3;lst={-1,a,b};Do[c=(a+b)+b;AppendTo[lst,c];a=b;b=c,{n,3*4!}];lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 13 2009]
%Y A078343 Cf. A000129.
%Y A078343 Sequence in context: A166302 A100342 A041281 this_sequence A148038 A148039 
               A148040
%Y A078343 Adjacent sequences: A078340 A078341 A078342 this_sequence A078344 A078345 
               A078346
%K A078343 sign
%O A078343 0,2
%A A078343 Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 22 2002
%E A078343 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 29 2004