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 A280237 Period length 8 sequence [0, 1, 0, 1, -1, 1, 0, 1, ...]. 1
 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1). FORMULA Euler transform of length 10 sequence [0, 1, -1, 0, 1, 0, 0, 1, 0, -1]. Moebius transform is length 8 sequence [1, -1, 0, -1, 0, 0, 0, 1]. a(n) is multiplicative with a(2) = 0, a(4) = -1, a(2^e) = 0 if e>2, a(p^e) = 1 if p>2. G.f.: x / (1 - x^2) - x^4 / (1 - x^8). G.f.: (x + x^3 - x^4 + x^5 + x^7) / (1 - x^8). G.f.: x * (1 - x^2) * (1 - x^5) * (1 - x^8) / ((1 - x^3) * (1 - x^10)). G.f.: x / (1 - x) - x^2 / (1 - x^2) - x^4 / (1 - x^4) + x^8 / (1 - x^8). G.f. A(x) = Sum_{k>0} F(x^k) where P(x) = x - x^2 - x^4 + x^8 = x * (1 - x^3) * (1 - x - x^4). a(n) = a(-n) = a(n+8) for all n in Z. a(n) = -(-1)^n * A259044(n). a(2*n + 1) = 1. a(4*n + 2) = 0. a(8*n) = 0. a(8*n + 4) = -1. EXAMPLE G.f. = x + x^3 - x^4 + x^5 + x^7 + x^9 + x^11 - x^12 + x^13 + x^15 + ... MATHEMATICA a[ n_] := Mod[n, 2] - Boole[ Mod[n, 8] == 4]; a[ n_] := {0, 1, 0, 1, -1, 1, 0, 1}[[Mod[n, 8] + 1]]; a[ n_] := SeriesCoefficient[ x / (1 - x^2) - x^4 / (1 - x^8), {x, 0, Abs@n}]; PROG (PARI) {a(n) = n%2 - (n%8==4)}; (PARI) {a(n) = [0, 1, 0, 1, -1, 1, 0, 1][n%8 + 1]}; (PARI) {a(n) = 1 - (n%2==0) - (n%4==0) + (n%8==0)}; (PARI) {a(n) = polcoeff( x / (1 - x^2) - x^4 / (1 - x^8) + x * O(x^abs(n)), abs(n))}; (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 +x^2-x^3+x^4+x^6)/(1-x^8))); // G. C. Greubel, Jul 29 2018 CROSSREFS Cf. A259044. Sequence in context: A157412 A023532 A030308 * A259044 A112690 A115971 Adjacent sequences:  A280234 A280235 A280236 * A280238 A280239 A280240 KEYWORD sign,mult,easy AUTHOR Michael Somos, Dec 29 2016 STATUS approved

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Last modified August 21 06:23 EDT 2018. Contains 313934 sequences. (Running on oeis4.)