%I A004119 M3308
%S A004119 1,4,7,13,25,49,97,193,385,769,1537,3073,6145,12289,24577,49153,98305,
               196609,
%T A004119 393217,786433,1572865,3145729,6291457,12582913,25165825,50331649,100663297,
%U A004119 201326593,402653185,805306369,1610612737,3221225473,6442450945,12884901889
%N A004119 3*2^n + 1. Alternatively, define the sequence S(a_0,a_1) by a_{n+2} is 
               the least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 
               0. This is S(4,7).
%C A004119 Also Pisot sequence L(4,7) (cf. A008776).
%C A004119 a(n) = number of terms of the arithmetic progression with first term 
               2^(2n-1) and last term 2^(2n+1). So common difference is 2^n. e.g. 
               a(2)=7 corresponds to (8,12,16,20,24,28,32). - Augustine O. Munagi 
               (amunagi(AT)yahoo.com), Feb 21 2007
%D A004119 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004119 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A004119 D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, 
               Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. 
               Publ., Oxford Univ. Press, New York, 1993;.
%D A004119 S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 
               657-663.
%D A004119 A. O. Munagi and T. Shonhiwa, On the partitions of a number into arithmetic 
               progressions, J. Integer Seq. 11 (2008), Article 08.5.4. [From Augustine 
               O. Munagi (amunagi(AT)yahoo.com), Jan 08 2009]
%H A004119 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A004119 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A004119 A. O. Munagi and T. Shonhiwa, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/index.html"> On the partitions of a number into arithmetic progressions</
               a>, J. Integer Sequences, 11 (2008), #08.5.4. [From Augustine O. 
               Munagi (amunagi(AT)yahoo.com), Jan 08 2009]
%F A004119 a(n) = 3a(n-1) - 2a(n-2).
%F A004119 For n>3, a(3)=13, a(n)= a(n-1)+2*floor(a(n-1)/2). - Benoit Cloitre, Aug 
               14, 2002.
%F A004119 For n>=1, a(n) = A049775(n+1)/2^(n-2). For n>=2, a(n) = 2a(n-1)-1; see 
               also A000051. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 
               2004
%F A004119 O.g.f.: -(-1-x+3*x^2)/((2*x-1)*(x-1)) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 23 2007
%p A004119 A004119:=-(-1-z+3*z**2)/(2*z-1)/(z-1); [S. Plouffe in his 1992 dissertation.]
%Y A004119 A049988 [From Augustine O. Munagi (amunagi(AT)yahoo.com), Jan 08 2009]
%Y A004119 Sequence in context: A000288 A074863 A118334 this_sequence A074864 A074865 
               A072683
%Y A004119 Adjacent sequences: A004116 A004117 A004118 this_sequence A004120 A004121 
               A004122
%K A004119 nonn,easy
%O A004119 0,2
%A A004119 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy