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Search: id:A001634
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| A001634 |
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a(n) = a(n-2) + a(n-3) + a(n-4).
(Formerly M0746 N0281)
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+0
1
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| 0, 2, 3, 6, 5, 11, 14, 22, 30, 47, 66, 99, 143, 212, 308, 454, 663, 974, 1425, 2091, 3062, 4490, 6578, 9643, 14130, 20711, 30351, 44484, 65192, 95546, 140027, 205222, 300765, 440795, 646014, 946782, 1387574, 2033591, 2980370, 4367947, 6401535
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
E.-B. Escott, Reply to Query 1484, L'Interm\'{e}diaire des Math\'{e}maticiens, 8 (1901), 63-64.
Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x(2+3x+4x^2)/(1-x^2-x^3-x^4).
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MAPLE
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A001634:=-z*(2+3*z+4*z**2)/(1+z)/(z**3+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
(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]
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PROGRAM
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(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))
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CROSSREFS
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Cf. A013979.
Adjacent sequences: A001631 A001632 A001633 this_sequence A001635 A001636 A001637
Sequence in context: A133477 A039653 A106379 this_sequence A095113 A002517 A053570
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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