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 A163811 Expansion of (1 - x) * (1 - x^10) / ((1 - x^5) * (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 10 sequence [ -1, 0, 0, 0, 1, 1, 0, 0, 0, -1]. a(2*n) = a(3*n) = 0 unless n=0, a(6*n + 1) = -1, a(6*n + 5) = 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). 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 A163817(n) = -a(n) unless n=0. A163817(n) = (-1)^n * a(n). Convolution inverse of A163812. Sequence in context: A143064 A185124 A185125 * A163817 A266837 A321081 Adjacent sequences:  A163808 A163809 A163810 * A163812 A163813 A163814 KEYWORD sign,easy AUTHOR Michael Somos, Aug 04 2009, Aug 09 2009 STATUS approved

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Last modified January 19 16:18 EST 2019. Contains 319307 sequences. (Running on oeis4.)