(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a112300 Showing 1-1 of 1 %I A112300 #9 Jul 09 2019 13:53:18 %S A112300 1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1, %T A112300 0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2, %U A112300 -1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0,2,-1,0,1,-2,0 %N A112300 Expansion of x * (1 - x)^2 * (1 - x^2) / (1 - x^6) in powers of x. %F A112300 Euler transform of length 6 sequence [ -2, -1, 0, 0, 0, 1]. %F A112300 Multiplicative with a(2^e) = 2*(-1)^e if e>0, a(3^e) = 0 if e>0, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6). %F A112300 G.f.: x * (1 - x)^2 / ((1 - x + x^2) * (1 + x + x^2)). - _Michael Somos_, May 04 2015 %F A112300 G.f.: -(f(x) + 3*f(-x)) / 2 where f(x) := x / (1 - x + x^2). - _Michael Somos_, May 04 2015 %F A112300 a(n) = -a(3 - n) = a(n+6), a(3*n) = 0 for all n in Z. %e A112300 G.f. = x - 2*x^2 + 2*x^4 - x^5 + x^7 - 2*x^8 + 2*x^10 - x^11 + x^13 - 2*x^14 + ... %t A112300 a[ n_] := {0, 1, -2, 0, 2, -1} [[ Mod[n, 6] + 1]]; (* _Michael Somos_, May 04 2015 *) %t A112300 PadRight[{},120,{1,-2,0,2,-1,0}] (* _Harvey P. Dale_, Jul 09 2019 *) %o A112300 (PARI) {a(n) = [0, 1, -2, 0, 2, -1][n%6 + 1]}; %K A112300 sign,easy,mult %O A112300 1,2 %A A112300 _Michael Somos_, Sep 02 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE