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 A001635 A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7. (Formerly M0762 N0289) 1
 0, 2, 3, 6, 10, 11, 21, 30, 48, 72, 110, 171, 260, 401, 613, 942, 1445, 2216, 3401, 5216, 8004, 12278, 18837, 28899, 44335, 68018, 104349, 160089, 245601, 376791, 578057, 886830, 1360538, 2087279, 3202216, 4912704, 7536863, 11562737, 17739062, 27214520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is an application of the general formula that Paul Barry gives for sequence A000129 to the subsequence of odd-indexed terms. - Pat Costello (pat.costello(AT)eku.edu), May 20 2003 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. Daniel C. Fielder, Errata:Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70. D. Fielder, Letter to N. J. A. Sloane, Jun. 1991 D. C. Fielder and C. O. Alford, Simulation concepts for studying incomplete (but potentially recursive) sequences, IASTED International Symposium Simulation and Modeling '89, Lugano, Switzerland, June 19-22, 1989. (Annotated scanned copy) Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, -1). FORMULA G.f.: x^2*(2 + x + x^2 + x^3 - 5*x^4)/(1 - x - x^2 + x^6). a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5), n >= 6. a(n) = Sum_{k=0..n} C(2*n+1, 2*k+1) * 2^k. - Pat Costello (pat.costello(AT)eku.edu), May 20 2003 MAPLE A001635:=-z*(2+3*z+4*z**2+5*z**3)/(-1+z**2+z**3+z**4+z**5); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation (Maple) a := n -> (Matrix([[5, -1\$3, 3, 4]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [1\$2, 0\$3, -1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=1..39);  # Alois P. Heinz, Aug 01 2008 MATHEMATICA LinearRecurrence[{1, 1, 0, 0, 0, -1}, {0, 2, 3, 6, 10, 11}, 50] (* T. D. Noe, Aug 09 2012 *) PROG (PARI) a(n)=if(n<0, 0, polcoeff(x^2*(2+x+x^2+x^3-5*x^4)/(1-x-x^2+x^6)+x*O(x^n), n)) (MAGMA) I:=[0, 2, 3, 6, 10, 11]; [n le 6 select I[n] else Self(n-1) + Self(n-2) - Self(n-6): n in [1..30]]; // G. C. Greubel, Jan 09 2018 CROSSREFS Cf. A000129. Sequence in context: A112925 A193246 A239012 * A106172 A189478 A090695 Adjacent sequences:  A001632 A001633 A001634 * A001636 A001637 A001638 KEYWORD nonn AUTHOR EXTENSIONS Edited by Michael Somos, Feb 17 2002 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)