Search: id:A001635
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%I A001635 M0762 N0289
%S A001635 0,2,3,6,10,11,21,30,48,72,110,171,260,401,613,942,1445,2216,3401,
%T A001635 5216,8004,12278,18837,28899,44335,68018,104349,160089,245601,376791,
%U A001635 578057,886830,1360538,2087279,3202216,4912704,7536863,11562737,17739062
%N A001635 A Fielder sequence: a(n)=a(n-1)+a(n-2)-a(n-6), n>=7.
%C A001635 This is an application of the general formula that Paul Barry gives for 
               sequence A000129 to the subsequence of odd-indexed terms. - Pat Costello 
               (pat.costello(AT)eku.edu), May 20 2003
%D A001635 Fielder, Daniel C.; Special integer sequences controlled by three parameters. 
               Fibonacci Quart 6 1968 64-70.
%D A001635 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001635 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001635 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 A001635 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 A001635 G.f.: x^2*(2+x+x^2+x^3-5*x^4)/(1-x-x^2+x^6).
%F A001635 a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5), n>=6.
%F A001635 a(n)=sum{k=0, ..n, C(2n+1, 2k+1)2^k}. - Pat Costello (pat.costello(AT)eku.edu), 
               May 20 2003
%p A001635 A001635:=-z*(2+3*z+4*z**2+5*z**3)/(-1+z**2+z**3+z**4+z**5); [Conjectured 
               (correctly) by S. Plouffe in his 1992 dissertation.]
%p A001635 (Maple) a := n -> (Matrix([[5,-1$3,3,4]]). Matrix(6, (i,j)-> if (i=j-1) 
               then 1 elif j=1 then [1$2,0$3,-1][i] else 0 fi)^n)[1,1] ; seq (a(n), 
               n=1..39); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 
               2008]
%o A001635 (PARI) a(n)=if(n<0,0,polcoeff(x^2*(2+x+x^2+x^3-5*x^4)/(1-x-x^2+x^6)+x*O(x^n),
               n))
%Y A001635 Cf. A000129.
%Y A001635 Sequence in context: A047402 A088196 A112925 this_sequence A106172 A090695 
               A104074
%Y A001635 Adjacent sequences: A001632 A001633 A001634 this_sequence A001636 A001637 
               A001638
%K A001635 nonn
%O A001635 1,2
%A A001635 N. J. A. Sloane (njas(AT)research.att.com).
%E A001635 Edited by Michael Somos, Feb 17, 2002

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