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Search: id:A003410
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| A003410 |
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Expansion of (1+x)(1+x^2)/(1-x-x^3).
(Formerly M0648)
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+0
5
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| 1, 2, 3, 5, 7, 10, 15, 22, 32, 47, 69, 101, 148, 217, 318, 466, 683, 1001, 1467, 2150, 3151, 4618, 6768, 9919, 14537, 21305, 31224, 45761, 67066, 98290, 144051, 211117, 309407, 453458, 664575, 973982, 1427440, 2092015, 3065997
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
R. K. Guy, personal communication.
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LINKS
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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
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a(n) = a(n-1) + a(n-3) for n>3, see also A000930. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 26 2005
For n>1, a(n) = 2*A000930(n) + A000930(n-2). [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Sep 10 2008]
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MAPLE
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G:=series((1+x)*(1+x^2)/(1-x-x^3), x=0, 42): 1, seq(coeff(G, x^n), n=1..38);
A003410:=-(1+z)*(1+z**2)/(-1+z+z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Essentially the same as A058278 and A097333, partial sums and first differences of A058278, first and second differences of itself and A038718. Equals A038718(n+1) + 1, n>0.
Adjacent sequences: A003407 A003408 A003409 this_sequence A003411 A003412 A003413
Sequence in context: A011972 A160571 A076972 this_sequence A018133 A116975 A134792
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 11 2004
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