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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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5
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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).
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LINKS
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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
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); # 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))
(Magma) I:=[0, 2, 3, 6, 10, 17, 21]; [n le 7 select I[n] else Self(n-1) + Self(n-2) - Self(n-7): n in [1..30]]; // G. C. Greubel, Jan 09 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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