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 A259042 Period 8 sequence [0, 1, 1, 1, 2, 1, 1, 1, ...]. 2
 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1). FORMULA Euler transform of length 8 sequence [1, 0, 1, -1, 0, -1, 0, 1]. Moebius transform is length 8 sequence [1, 0, 0, 1, 0, 0, 0, -2]. a(n) is multiplicative with a(2) = 1, a(4) = 2, a(2^e) = 0 if e>2, a(p^e) = 1 if p>2. G.f.: x * (1 + x^3) / ((1 - x) * (1 + x^4)). G.f.: x * (1 - x^4) * (1 - x^6) / ((1 - x) * (1 - x^3) * (1 - x^8)). G.f.: 1 / (1 - x) - 1 / (1 + x^4). a(n) = a(-n) = a(n+8) for all n in Z. a(2*n + 1) = a(4*n + 2) = 1.  a(8*n) = 0. a(8*n + 4) = 2. a(n) = A257179(n+4) unless n = -4. a(n) = 1 + 1/8*[n mod 8 + (n+3) mod 8 - (n+4) mod 8 - (n+7) mod 8]. [Paolo P. Lava, Jun 24 2015] EXAMPLE G.f. = x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + x^7 + x^9 + x^10 + x^11 + ... MATHEMATICA a[ n_] := {1, 1, 1, 2, 1, 1, 1, 0}[[Mod[n, 8, 1]]]; a[ n_] := SeriesCoefficient[ 1 / (1 - x) - 1 / (1 + x^4), {x, 0, Abs@n}]; PROG (PARI) {a(n) = 1 + (n%4 == 0) - 2*(n%8 == 0)}; (PARI) {a(n) = [ 0, 1, 1, 1, 2, 1, 1, 1][n%8 + 1]}; (PARI) {a(n) = polcoeff( 1 / (1 - x) - 1 / (1 + x^4) + x * O(x^abs(n)), abs(n))}; CROSSREFS Cf. A010877, A257179. Sequence in context: A326695 A323191 A257179 * A333179 A240021 A087810 Adjacent sequences:  A259039 A259040 A259041 * A259043 A259044 A259045 KEYWORD nonn,mult,easy AUTHOR Michael Somos, Jun 17 2015 EXTENSIONS More terms from Antti Karttunen, Jul 29 2018 STATUS approved

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Last modified April 9 19:36 EDT 2020. Contains 333362 sequences. (Running on oeis4.)