Search: id:A001638
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%I A001638 M3351 N1348
%S A001638 4,1,1,4,9,11,16,29,49,76,121,199,324,521,841,1364,2209,3571,5776,9349,
%T A001638 15129,24476,39601,64079,103684,167761,271441,439204,710649,1149851,
%U A001638 1860496,3010349,4870849,7881196,12752041,20633239,33385284,54018521
%N A001638 A Fielder sequence: a(n)=a(n-1)+a(n-3)+a(n-4), n>=4.
%D A001638 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001638 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001638 Fielder, Daniel C.; Special integer sequences controlled by three parameters. 
               Fibonacci Quart 6 1968 64-70.
%H A001638 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 A001638 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 A001638 G.f.: (1-x)(4+x+x^2)/((1+x^2)(1-x-x^2)). a(n)=L(n)+i^n+(-i)^n, a(2n)=L(n)^2, 
               a(2n+1)=L(2n+1) where L() is Lucas sequence.
%p A001638 A001638:=-(z+1)*(4*z**2-z+1)/(z**2+z-1)/(z**2+1); [Conjectured by S. 
               Plouffe in his 1992 dissertation. Gives sequence except for the initial 
               4.]
%o A001638 (PARI) a(n)=if(n<0,0,fibonacci(n+1)+fibonacci(n-1)+simplify(I^n+(-I)^n))
%o A001638 (PARI) a(n)=if(n<0,0,polsym((1+x-x^2)*(1+x^2),n)[n+1])
%Y A001638 Sequence in context: A026998 A080061 A124258 this_sequence A133826 A122185 
               A136680
%Y A001638 Adjacent sequences: A001635 A001636 A001637 this_sequence A001639 A001640 
               A001641
%K A001638 nonn
%O A001638 0,1
%A A001638 N. J. A. Sloane (njas(AT)research.att.com).
%E A001638 Edited by Michael Somos, Feb 17 2002 and Nov 2 2002

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