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 A001636 A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8. (Formerly M0763 N0290) 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, -1). FORMULA 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. MAPLE 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 MATHEMATICA LinearRecurrence[{1, 1, 0, 0, 0, 0, -1}, {0, 2, 3, 6, 10, 17, 21}, 50] (* T. D. Noe, Aug 09 2012 *) PROG (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 CROSSREFS Cf. A013983. Sequence in context: A066895 A105075 A140669 * A036588 A334893 A239872 Adjacent sequences:  A001633 A001634 A001635 * A001637 A001638 A001639 KEYWORD nonn AUTHOR EXTENSIONS Edited by Michael Somos, Feb 17 2002 STATUS approved

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Last modified April 21 01:52 EDT 2021. Contains 343143 sequences. (Running on oeis4.)