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# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a134668 Showing 1-1 of 1 %I A134668 #27 Dec 12 2023 08:42:08 %S A134668 1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1, %T A134668 1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0, %U A134668 -1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1 %N A134668 Period 6: repeat [1, -1, 0, 0, -1, 1]. %C A134668 The Fi2 sums, see A180662, of triangle A108299 equal the terms of this sequence. - _Johannes W. Meijer_, Aug 11 2011 %H A134668 Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1). %F A134668 First differences of A134667. %F A134668 Euler transform of length 6 sequence [-1, 0, 0, -1, 0, 1]. - _Michael Somos_, Feb 08 2008 %F A134668 a(n) = a(-1-n) for all n in Z. - _Michael Somos_, Feb 08 2008 %F A134668 G.f.: (1-x)*(1-x^4) / (1-x^6) = (1-x)*(1+x^2) / ((1-x+x^2)*(1+x+x^2)) = (1-x+x^2-x^3) / (1+x^2+x^4). %F A134668 a(6*n + 2) = a(6*n + 3) = 0. - _Michael Somos_, Oct 16 2015 %F A134668 From _Wesley Ivan Hurt_, Jun 20 2016: (Start) %F A134668 a(n) + a(n-2) + a(n-4) = 0 for n>3. %F A134668 a(n) = cos(n*Pi/6) * (3*cos(n*Pi/2) + 2*sqrt(3)*sin(n*Pi/6) - 3*sqrt(3)*sin(n*Pi/2))/3. (End) %e A134668 G.f. = 1 - x - x^4 + x^5 + x^6 - x^7 - x^10 + x^11 + x^12 - x^13 - x^16 + ... %p A134668 A134668 :=proc(n): (1/6)*(-2*((n+1) mod 6)+((n+2) mod 6)-((n+4) mod 6)+2*((n+5) mod 6)) end: seq(A134668(n), n=0..74); # _Johannes W. Meijer_, Aug 14 2011 %t A134668 PadRight[{},120,{1,-1,0,0,-1,1}] (* or *) LinearRecurrence[{0,-1,0,-1},{1,-1,0,0},120] (* _Harvey P. Dale_, Dec 03 2012 *) %o A134668 (PARI) {a(n)=[1, -1, 0, 0, -1, 1][n%6+1]}; /* _Michael Somos_, Feb 08 2008 */ %o A134668 (Magma) &cat [[1, -1, 0, 0, -1, 1]^^20]; // _Wesley Ivan Hurt_, Jun 20 2016 %Y A134668 Cf. A108299, A134667, A180662. %K A134668 sign,easy %O A134668 0,1 %A A134668 _Paul Curtz_, Jan 26 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE