Search: id:A001636
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%I A001636 M0763 N0290
%S A001636 0,2,3,6,10,17,21,38,57,92,143,225,351,555,868,1366,2142,3365,5282,
%T A001636 8296,13023,20451,32108,50417,79160,124295,195159,306431,481139,755462,
%U A001636 1186184,1862486,2924375,4591702,7209646,11320209,17774393,27908418
%N A001636 A Fielder sequence: a(n)=a(n-1)+a(n-2)-a(n-7), n>=8.
%D A001636 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001636 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001636 Fielder, Daniel C.; Special integer sequences controlled by three parameters. 
               Fibonacci Quart 6 1968 64-70.
%H A001636 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 A001636 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 A001636 G.f.: x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7).
%F A001636 a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), n>=7.
%p A001636 A001636:=-z*(2+3*z+4*z**2+5*z**3+6*z**4)/(z+1)/(z**5+z**3+z-1); [S. Plouffe 
               in his 1992 dissertation.]
%p A001636 (Maple) a := n -> (Matrix([[6,-1$4,4,5]]). Matrix(7, (i,j)-> if (i=j-1) 
               then 1 elif j=1 then [1$2,0$4,-1][i] else 0 fi)^n)[1,1] ; seq (a(n), 
               n=1..38); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 
               2008]
%o A001636 (PARI) a(n)=if(n<0,0,polcoeff(x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7)+x*O(x^n),
               n))
%Y A001636 Cf. A013983.
%Y A001636 Sequence in context: A066895 A105075 A140669 this_sequence A036588 A099517 
               A026647
%Y A001636 Adjacent sequences: A001633 A001634 A001635 this_sequence A001637 A001638 
               A001639
%K A001636 nonn
%O A001636 1,2
%A A001636 N. J. A. Sloane (njas(AT)research.att.com).
%E A001636 Edited by Michael Somos, Feb 17, 2002

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