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 A164115 Expansion of (1 - x^5) / ((1 - x) * (1 - x^4)) in powers of x. 3
 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The sequence A107453 has the same terms but different offset. Convolution inverse of A164116. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). FORMULA Euler transform of length-5 sequence [ 1, 0, 0, 1, -1]. a(n) is multiplicative with a(2) = 1, a(2^e) = 2 if e>1, a(p^e) = 1 if p>2. a(n) = (-1)^n * A164117(n). a(4*n) = 2 unless n=0. a(2*n + 1) = a(4*n + 2) = 1. a(-n) = a(n). a(n+4) = a(n) unless n=0 or n=-4. G.f.: (1 + x + x^2 + x^3 + x^4) / (1 - x^4). a(n) = A138191(n+2), n>0. - R. J. Mathar, Aug 17 2009 Dirichlet g.f. (1+1/4^s)*zeta(s). - R. J. Mathar, Feb 24 2011 a(n) = (i^n + (-i)^n + (-1)^n + 5)/4 for n > 0 where i is the imaginary unit. - Bruno Berselli, Feb 25 2011 EXAMPLE 1 + x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + x^7 + 2*x^8 + x^9 + x^10 + ... MATHEMATICA CoefficientList[Series[(1+x+x^2+x^3+x^4)/(1-x^4), {x, 0, 100}], x] (* G. C. Greubel, Sep 22 2018 *) LinearRecurrence[{0, 0, 0, 1}, {1, 1, 1, 1, 2}, 120] (* or *) PadRight[{1}, 120, {2, 1, 1, 1}] (* Harvey P. Dale, Aug 24 2019 *) PROG (PARI) {a(n) = 2 - (n==0) - (n%4>0)} (PARI) x='x+O('x^99); Vec((1-x^5)/((1-x)*(1-x^4))) \\ Altug Alkan, Sep 23 2018 (MAGMA) m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x+x^2+x^3+x^4)/(1-x^4))); // G. C. Greubel, Sep 22 2018 CROSSREFS Cf. A107453, A138191, A164116, A164117. Sequence in context: A186006 A236398 A107453 * A164117 A177704 A138191 Adjacent sequences:  A164112 A164113 A164114 * A164116 A164117 A164118 KEYWORD nonn,mult,easy AUTHOR Michael Somos, Aug 10 2009 STATUS approved

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Last modified September 18 09:59 EDT 2019. Contains 327170 sequences. (Running on oeis4.)