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 A259044 Period 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, 1, 1, 0 (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 8 sequence [ 0, 1, 1, 0, -1, -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^5) * (1 + x^3) / ((1 - x^2) * (1 - x^8)). G.f.: x * (1 - x^5) * (1 - x^6) / ((1 - x^2) * (1 - x^3) * (1 - x^8)). G.f.: f(x) + f(x^4) where f(x) := x / (1 - x^2). a(n) = a(-n) = a(n+8) for all n in Z. a(n) = -(-1)^n * A280237(n). a(2*n + 1) = 1. a(4*n + 2) = 0. G.f.: -x*(x^2-x+1)*(x^4+x^3+x^2+x+1) / ( (x-1)*(1+x)*(x^2+1)*(x^4+1) ). - R. J. Mathar, Jun 18 2015 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_] := { 1, 0, 1, 1, 1, 0, 1, 0}[[Mod[n, 8, 1]]]; a[ n_] := SeriesCoefficient[ x / (1 - x^2) + x^4 / (1 - x^8), {x, 0, Abs@n}]; PadRight[{}, 120, {0, 1, 0, 1, 1, 1, 0, 1}] (* Harvey P. Dale, Feb 22 2018 *) 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) = polcoeff( x / (1 - x^2) + x^4 / (1 - x^8) + x * O(x^abs(n)), abs(n))}; CROSSREFS Cf. A280237. Sequence in context: A023532 A030308 A280237 * A112690 A115971 A072165 Adjacent sequences:  A259041 A259042 A259043 * A259045 A259046 A259047 KEYWORD nonn,mult,easy AUTHOR Michael Somos, Jun 17 2015 STATUS approved

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Last modified August 21 13:31 EDT 2018. Contains 313954 sequences. (Running on oeis4.)