Search: id:A001634
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%I A001634 M0746 N0281
%S A001634 0,2,3,6,5,11,14,22,30,47,66,99,143,212,308,454,663,974,1425,2091,3062,
%T A001634 4490,6578,9643,14130,20711,30351,44484,65192,95546,140027,205222,
%U A001634 300765,440795,646014,946782,1387574,2033591,2980370,4367947,6401535
%N A001634 a(n) = a(n-2) + a(n-3) + a(n-4).
%D A001634 E.-B. Escott, Reply to Query 1484, L'Interm\'{e}diaire des Math\'{e}maticiens, 
               8 (1901), 63-64.
%D A001634 Fielder, Daniel C.; Special integer sequences controlled by three parameters. 
               Fibonacci Quart 6 1968 64-70.
%D A001634 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001634 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001634 T. D. Noe, <a href="b001634.txt">Table of n, a(n) for n=0..500</a>
%H A001634 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 A001634 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 A001634 G.f.: x(2+3x+4x^2)/(1-x^2-x^3-x^4).
%p A001634 A001634:=-z*(2+3*z+4*z**2)/(1+z)/(z**3+z-1); [S. Plouffe in his 1992 
               dissertation.]
%p A001634 (Maple) a := n -> (Matrix([[0,4,-1,-1]]). Matrix(4, (i,j)-> if (i=j-1) 
               then 1 elif j=1 then [0,1,1,1][i] else 0 fi)^n)[1,1] ; seq (a(n), 
               n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 
               2008]
%o A001634 (PARI) a(n)=if(n<0,0,polcoeff(x*(2+3*x+4*x^2)/(1-x^2-x^3-x^4)+x*O(x^n),
               n))
%Y A001634 Cf. A013979.
%Y A001634 Sequence in context: A133477 A039653 A106379 this_sequence A095113 A002517 
               A053570
%Y A001634 Adjacent sequences: A001631 A001632 A001633 this_sequence A001635 A001636 
               A001637
%K A001634 nonn,easy,nice
%O A001634 0,2
%A A001634 N. J. A. Sloane (njas(AT)research.att.com).

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