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 A163812 Expansion of (1 - x^5) * (1 - x^6) / ((1 - x) * (1 - x^10)) in powers of x. 4
 1, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1 (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 (1,-1,1,-1). FORMULA Euler transform of length 10 sequence [ 1, 0, 0, 0, -1, -1, 0, 0, 0, 1]. a(5*n) = 0 unless n=0. a(n) = -a(-n) unless n=0. a(n+5) = -a(n) unless n=0 or n=-5. G.f.: (1 + x^2 + x^4) / (1 - x + x^2 - x^3 + x^4). a(n) = (-1)^n * A163818(n). Convolution inverse of A163811. G.f.: A(x) = 1 / (1 - x / ( 1 + x^4 / (1 + x^2))) = 1 + x / (1 - x / (1 + x^3 / (1 + x^2 / (1 + x / (1 - x))))). - Michael Somos, Jan 03 2013 a(n) = A099443(n-1), n>0. - R. J. Mathar, Aug 05 2009 EXAMPLE G.f. = 1 + x + x^2 + x^3 + x^4 - x^6 - x^7 - x^8 - x^9 + x^11 + x^12 + x^13 + ... MATHEMATICA a[ n_] := Boole[n == 0] + (-1)^Quotient[n, 5] Sign@Mod[n, 5]; (* Michael Somos, Jun 17 2015 *) PROG (PARI) {a(n) = (n==0) + [0, 1, 1, 1, 1, 0, -1, -1, -1, -1][n%10 + 1]}; CROSSREFS Cf. A099443, A163811, A163818. Sequence in context: A344880 A167020 A236862 * A163818 A345009 A071040 Adjacent sequences: A163809 A163810 A163811 * A163813 A163814 A163815 KEYWORD sign,easy AUTHOR Michael Somos, Aug 04 2009 STATUS approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)