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 A188578 Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x. 0
 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS FORMULA Euler transform of length 15 sequence [ 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1]. a(n) = b(2*n + 1) where b(n) is multiplicative with b(p^e) = 0^e if p<7, b(p^e) = 1, if p == 1, 17, 19, 23 (mod 30), b(p^e) = (-1)^e if p == 7, 11, 13, 29 (mod 30). G.f.: (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15). a(-1 - n) = -a(n). G.f.: (1-x)^2 *(1+x) *(1+x+x^2) *(1-x+x^2) / (1-x+x^3-x^4+x^5-x^7+x^8). - R. J. Mathar, Apr 09 2011 a(n) = -a(-1-n) = a(n+15) for all n in Z. - Michael Somos, May 21 2015 a(2*n) = a(n-4), a(2*n + 1) = a(n+4), a(3*n) = A080891(n+1), a(3*n + 1) = 0, a(3*n + 2) = -A080891(n) for all n in Z. - Michael Somos, May 21 2015 EXAMPLE G.f. = 1 - x^3 - x^5 - x^6 + x^8 + x^9 + x^11 - x^14 + x^15 - x^18 - x^20 + ... G.f. = q - q^7 - q^11 - q^13 + q^17 + q^19 + q^23 - q^29 + q^31 - q^37 - q^41 + ... MATHEMATICA a[ n_] := KroneckerSymbol[ -60, 2 n + 1]; PROG (PARI) {a(n) = kronecker( -60, 2*n + 1)}; CROSSREFS Cf. A080891. Sequence in context: A010059 A143580 A011749 * A104105 A143221 A126999 Adjacent sequences:  A188575 A188576 A188577 * A188579 A188580 A188581 KEYWORD sign AUTHOR Michael Somos, Apr 04 2011 STATUS approved

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