%I A048578
%S A048578 3,5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537,131073,
%T A048578 262145,524289,1048577,2097153,4194305,8388609,16777217,33554433,67108865,
%U A048578 134217729,268435457,536870913,1073741825,2147483649,4294967297,8589934593
%N A048578 Pisot sequence L(3,5).
%D A048578 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H A048578 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Arithmetic and growth of periodic orbits</a>, J. Integer 
               Seqs., Vol. 4 (2001), #01.2.1.
%F A048578 a(n) = 2^(n+1)+1. a(n) = 3a(n-1) - 2a(n-2).
%F A048578 O.g.f.: -1/(-1+x)-2/(-1+2*x) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 23 2007
%p A048578 a:=n->sum(binomial(n,k)+binomial(k,n), k=0..n): seq(a(n), n=1..33); - 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
%o A048578 (Other) sage: [gaussian_binomial(n,1,2)+2 for n in xrange(1,34)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
%Y A048578 Essentially the same as A000079.
%Y A048578 Subsequence of A000051. See A008776 for definitions of Pisot sequences.
%Y A048578 Sequence in context: A135728 A083318 A127904 this_sequence A087312 A099170 
               A018095
%Y A048578 Adjacent sequences: A048575 A048576 A048577 this_sequence A048579 A048580 
               A048581
%K A048578 nonn
%O A048578 0,1
%A A048578 David W. Wilson (davidwwilson(AT)comcast.net)