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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

N. J. A. Sloane

EXTENSIONS

Edited by Michael Somos, Feb 17 2002

STATUS

approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)