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A001635
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A Fielder sequence: a(n)=a(n-1)+a(n-2)-a(n-6), n>=7.
(Formerly M0762 N0289)
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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
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REFERENCES
| Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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
| S. 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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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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(2n+1, 2k+1)2^k}. - Pat Costello (pat.costello(AT)eku.edu), May 20 2003
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MAPLE
| A001635:=-z*(2+3*z+4*z**2+5*z**3)/(-1+z**2+z**3+z**4+z**5); [Conjectured (correctly) by S. 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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]
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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))
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CROSSREFS
| Cf. A000129.
Sequence in context: A047402 A088196 A112925 * A106172 A189478 A090695
Adjacent sequences: A001632 A001633 A001634 * A001636 A001637 A001638
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Michael Somos, Feb 17, 2002
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