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 A280560 a(n) = (-1)^n * 2 if n!=0, with a(0) = 1. 4
 1, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (-1). FORMULA Euler transform of length 2 sequence [-2, 1]. Moebius transform is length 2 sequence [-2, 4]. a(n) = -2*A033999(n) if n!=0. G.f.: (1 - x) / (1 + x) = 1 / (1 + 2*x / (1 - x)) = 1 - 2*x / (1 + x). E.g.f.: 2*exp(-x) - 1. a(n) = a(-n) for all n in Z. a(n) = A084100(2*n) = A084100(2*n + 1), if n>=0. a(n) = (-1)^n * A040000(n). a(2*n) = A040000(n). Convolution inverse is A040000. EXAMPLE G.f. = 1 - 2*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 2*x^7 + 2*x^8 - 2*x^9 + ... MATHEMATICA a[ n_] := (-1)^n (2 - Boole[n == 0]); PadRight[{1}, 120, {2, -2}] (* Harvey P. Dale, Jun 04 2019 *) PROG (PARI) {a(n) = (-1)^n * if(n, 2, 1)}; (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x)/(1+x))); // G. C. Greubel, Jul 29 2018 CROSSREFS Cf. A033999, A040000, A084100. Sequence in context: A004218 A044931 A178487 * A044932 A211662 A211669 Adjacent sequences:  A280557 A280558 A280559 * A280561 A280562 A280563 KEYWORD sign AUTHOR Michael Somos, Jan 05 2017 STATUS approved

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Last modified July 21 06:53 EDT 2019. Contains 325192 sequences. (Running on oeis4.)