Search: id:A003410
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%I A003410 M0648
%S A003410 1,2,3,5,7,10,15,22,32,47,69,101,148,217,318,466,683,1001,1467,2150,
%T A003410 3151,4618,6768,9919,14537,21305,31224,45761,67066,98290,144051,211117,
%U A003410 309407,453458,664575,973982,1427440,2092015,3065997
%N A003410 Expansion of (1+x)(1+x^2)/(1-x-x^3).
%D A003410 R. K. Guy, personal communication.
%D A003410 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003410 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 A003410 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 A003410 a(n) = a(n-1) + a(n-3) for n>3, see also A000930. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 26 2005
%F A003410 For n>1, a(n) = 2*A000930(n) + A000930(n-2). [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), 
               Sep 10 2008]
%p A003410 G:=series((1+x)*(1+x^2)/(1-x-x^3),x=0,42): 1,seq(coeff(G,x^n),n=1..38);
%p A003410 A003410:=-(1+z)*(1+z**2)/(-1+z+z**3); [S. Plouffe in his 1992 dissertation.]
%Y A003410 Essentially the same as A058278 and A097333, partial sums and first differences 
               of A058278, first and second differences of itself and A038718. Equals 
               A038718(n+1) + 1, n>0.
%Y A003410 Sequence in context: A011972 A160571 A076972 this_sequence A018133 A116975 
               A134792
%Y A003410 Adjacent sequences: A003407 A003408 A003409 this_sequence A003411 A003412 
               A003413
%K A003410 nonn,easy
%O A003410 0,2
%A A003410 N. J. A. Sloane (njas(AT)research.att.com).
%E A003410 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 11 2004

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