Search: id:A048573
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%I A048573
%S A048573 2,3,7,13,27,53,107,213,427,853,1707,3413,6827,13653,27307,54613,
%T A048573 109227,218453,436907,873813,1747627,3495253,6990507,13981013,27962027,
%U A048573 55924053,111848107,223696213,447392427,894784853,1789569707
%N A048573 a(n) = a(n-1) + 2a(n-2), a(0)=2, a(1)=3.
%C A048573 Number of positive integers requiring exactly n signed bits in the modified 
               non-adjacent form representation. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Aug 02 2003
%C A048573 The n-th entry (n>1) of the sequence is equal to the 1,1-entry of the 
               n-th power of the unnormalized 4 by 4 Haar matrix: [1 1 1 0 / 1 1 
               -1 0 / 1 1 0 1 / 1 1 0 -1]. - Simone Severini (ss54(AT)york.ac.uk), 
               Oct 27 2004
%H A048573 W. Bosma, <a href="http://almira.math.u-bordeaux.fr/jtnb/2001-1/jtnb13-1.html#jourelec">
               Signed bits and fast exponentiation</a>
%F A048573 G.f.: (2+x)/(1-x-2x^2).
%F A048573 a(n) = (5*2^n+(-1)^n)/3
%F A048573 a(n)=2*A001045(n+1)+A001045(n) (note that 2 is the limit of A001045(n+1)/
               A001045(n)). [From Paul Barry (pbarry(AT)wit.ie), Sep 14 2009]
%o A048573 (PARI) a(n)=if(n<0,0,(5*2^n+(-1)^n)/3)
%o A048573 (PARI) a(n)=if(n<0,0,if(n<2,n+2,a(n-1)+2*a(n-2)))
%Y A048573 a(n) = 2^(n+1)-A001045(n).
%Y A048573 a(n) = A084170(n)+1 = |A083581(n)-3| = A081254(n+1)-A081254(n) = A084214(n+2)/
               2.
%Y A048573 Sequence in context: A128695 A024504 A088172 this_sequence A006946 A074129 
               A055003
%Y A048573 Adjacent sequences: A048570 A048571 A048572 this_sequence A048574 A048575 
               A048576
%K A048573 nonn
%O A048573 0,1
%A A048573 Michael Somos

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