Search: id:A001610
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%I A001610 M0764 N0291
%S A001610 0,2,3,6,10,17,28,46,75,122,198,321,520,842,1363,2206,3570,5777,9348,
%T A001610 15126,24475,39602,64078,103681,167760,271442,439203,710646,1149850,
%U A001610 1860497,3010348,4870846,7881195,12752042,20633238,33385281,54018520
%N A001610 a(n) = a(n-1) + a(n-2) + 1.
%C A001610 For prime p, p divides a(p-1). [From T. D. Noe (noe(AT)sspectra.com), 
               Apr 11 2009]
%D A001610 D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.
%D A001610 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001610 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001610 J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime 
               constant, Math. Comp., 15 (1961), 396-398.
%H A001610 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 A001610 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.
%F A001610 a(n) = A000204(n)-1 = A000032(n+1)-1 = A000071(n+1)+A000045(n)
%F A001610 a(n)=F(n)+F(n+2)-1 {where F(n) is the n-th Fibonacci number} - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
%F A001610 a(n) = A014217(n+1)- A000035(n+1). - Paul Curtz (bpcrtz(AT)free.fr), 
               Sep 21 2008
%F A001610 a(n)=-1+(1/2)*[1/2+(1/2)*sqrt(5)]^n+(1/2)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(1/
               2)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+(1/2)*[1/2-(1/2)*sqrt(5)]^n, with 
               n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 29 2008]
%p A001610 A001610:=-z*(-2+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%p A001610 with(combinat): seq(fibonacci(n)+fibonacci(n+2)-1, n=0..36); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
%p A001610 g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-1, 
               n=1..37);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 
               09 2009]
%Y A001610 Cf. A001610, A000032, A000204.
%Y A001610 Sequence in context: A026647 A026669 A023614 this_sequence A135431 A123908 
               A026397
%Y A001610 Adjacent sequences: A001607 A001608 A001609 this_sequence A001611 A001612 
               A001613
%K A001610 nonn
%O A001610 0,2
%A A001610 N. J. A. Sloane (njas(AT)research.att.com).
%E A001610 More terms from Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000

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