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 A163817 Expansion of (1 - x^2) * (1 - x^5) / ((1 - x) * (1 - x^6)) in powers of x. 3
 1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0, -1, 0, -1). FORMULA Euler transform of length 6 sequence [ 1, -1, 0, 0, -1, 1]. a(n) is multiplicative with a(2^e) = a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6). a(2*n) = a(3*n) = 0 unless n=0, a(6*n + 5) = -1, a(6*n + 1) = a(0) = 1. a(-n) = -a(n) unless n=0. a(n+6) = a(n) unless n=0 or n=-6. G.f.: (1 + x + x^2 + x^3 + x^4) / (1 + x^2 + x^4). a(n) = A134667(n), n>0. - R. J. Mathar, Aug 05 2009 G.f. A(x) = 1 + x / (1 + x^4 / (1 + x^2)) = 1 / (1 - x / (1 + x / (1 - x^3 / (1 + x^2 / (1 - x / (1 + x)))))) . - Michael Somos, Jan 03 2013 EXAMPLE 1 + x - x^5 + x^7 - x^11 + x^13 - x^17 + x^19 - x^23 + x^25 - x^29 + ... MATHEMATICA Join[{1}, LinearRecurrence[{0, -1, 0, -1}, {1, 0, 0, 0}, 50]] (* G. C. Greubel, Aug 04 2017 *) PROG (PARI) {a(n) = (n==0) + [0, 1, 0, 0, 0, -1][n%6 + 1]} (PARI) {a(n) = (n==0) + kronecker(-12, n)} CROSSREFS A163811(n) = -a(n) unless n=0. A163811(n) = (-1)^n * a(n). Convolution inverse of A163818. Sequence in context: A185125 A327580 A163811 * A266837 A321081 A267126 Adjacent sequences: A163814 A163815 A163816 * A163818 A163819 A163820 KEYWORD sign,easy,mult AUTHOR Michael Somos, Aug 04 2009 STATUS approved

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Last modified July 21 20:59 EDT 2024. Contains 374475 sequences. (Running on oeis4.)