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 A165192 a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (1, 0, -1). FORMULA a(n) = (-1)^n*A104771(n). G.f.: (1+x+x^2)/(1-x+x^3). EXAMPLE 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. MATHEMATICA LinearRecurrence[{1, 0, -1}, {1, 2, 3}, 80] (* Harvey P. Dale, Apr 13 2012 *) PROG (Python) series = [1, 2, 3] for i in range(2, 30): .series.append((series[i] - series[i-1])+(series[i-1]-series[i-2])) print series CROSSREFS Cf. A104771 Sequence in context: A269735 A056619 A239579 * A104771 A056888 A286297 Adjacent sequences:  A165189 A165190 A165191 * A165193 A165194 A165195 KEYWORD easy,sign AUTHOR Ben Paul Thurston, Sep 06 2009 EXTENSIONS Offset corrected and recurrence simplified by R. J. Mathar, Sep 08 2009 More terms from Harvey P. Dale, Apr 13 2012 STATUS approved

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