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A001636
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A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8.
(Formerly M0763 N0290)
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1
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0, 2, 3, 6, 10, 17, 21, 38, 57, 92, 143, 225, 351, 555, 868, 1366, 2142, 3365, 5282, 8296, 13023, 20451, 32108, 50417, 79160, 124295, 195159, 306431, 481139, 755462, 1186184, 1862486, 2924375, 4591702, 7209646, 11320209, 17774393, 27908418, 43820325
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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 = 1..1000
_Simon 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.
_Simon 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*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7).
a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), n>=7.
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MAPLE
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A001636:=-z*(2+3*z+4*z**2+5*z**3+6*z**4)/(z+1)/(z**5+z**3+z-1); [Simon Plouffe in his 1992 dissertation.]
(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, Aug 01 2008]
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MATHEMATICA
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LinearRecurrence[{1, 1, 0, 0, 0, 0, -1}, {0, 2, 3, 6, 10, 17, 21}, 50] (* T. D. Noe, Aug 09 2012 *)
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PROG
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(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))
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CROSSREFS
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Cf. A013983.
Sequence in context: A066895 A105075 A140669 * A036588 A099517 A026647
Adjacent sequences: A001633 A001634 A001635 * A001637 A001638 A001639
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Edited by Michael Somos, Feb 17, 2002
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STATUS
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approved
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