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A165192
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a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3).
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0
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1, 2, 3, 2, 0, -3, -5, -5, -2, 3, 8, 10, 7, -1, -11, -18, -17, -6, 12, 29, 35, 23, -6, -41, -64, -58, -17, 47, 105, 122, 75, -30, -152, -227, -197, -45, 182, 379, 424, 242, -137, -561, -803, -666, -105, 698, 1364, 1469, 771, -593, -2062, -2833, -2240, -178
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..53.
Index entries for linear recurrences with constant coefficients, signature (1,0,-1).
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FORMULA
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a(n) = (-1)^n*A104771(n).
G.f.: (1+x+x^2)/(1-x+x^3).
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EXAMPLE
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a(3) = 2 because 2 = 3 - 1 where the 1, 3 on the right of the equals sign are the first and third terms of the series.
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MATHEMATICA
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LinearRecurrence[{1, 0, -1}, {1, 2, 3}, 80] (* Harvey P. Dale, Apr 13 2012 *)
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PROG
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(Python)
series = [1, 2, 3]
for i in range(2, 30):
series.append(series[i] - series[i - 2])
print(series)
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CROSSREFS
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Cf. A104771
Sequence in context: A303121 A332921 A239579 * A104771 A307688 A056888
Adjacent sequences: A165189 A165190 A165191 * A165193 A165194 A165195
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KEYWORD
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easy,sign
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AUTHOR
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Ben Paul Thurston, Sep 06 2009
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EXTENSIONS
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Offset corrected and recurrence simplified by R. J. Mathar, Sep 08 2009
More terms from Harvey P. Dale, Apr 13 2012
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STATUS
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approved
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