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 A178141 Period 6: repeat [4, -1, 2, -4, 1, 2]. 2
 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Differences of the period 6: repeat [1, 5, 4, 6, 2, 3] (A070365). LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1). FORMULA Mix A153727(n+1) with -A153727(n). a(n) = (1/6)*{-6*(n mod 6)+3*[(n+1) mod 6]-5*[(n+2) mod 6]+6*[(n+3) mod 6]-3*[(n+4) mod 6]+5*[(n+5) mod 6]}. [Paolo P. Lava, May 24 2010] From Wesley Ivan Hurt, Jun 23 2016: (Start) G.f.: (4-x+2*x^2-4*x^3+x^4+2*x^5)/(1-x^6). a(n) = a(n-6) for n>5. a(n) = (2 + 5*cos(n*Pi) + 7*cos(n*Pi/3) - 2*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3))/3. (End) MAPLE A178141:=n->[4, -1, 2, -4, 1, 2][(n mod 6)+1]: seq(A178141(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016 MATHEMATICA PadRight[{}, 100, {4, -1, 2, -4, 1, 2}] (* Wesley Ivan Hurt, Jun 23 2016 *) PROG (PARI) a(n)=[1, 5, 4, 6, 2, 3][n%5+1] \\ Charles R Greathouse IV, Jun 02 2011 (MAGMA) &cat [[4, -1, 2, -4, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016 CROSSREFS Cf. A069705, A070365, A132954, A153727. Sequence in context: A072033 A100353 A080508 * A063987 A236269 A010126 Adjacent sequences:  A178138 A178139 A178140 * A178142 A178143 A178144 KEYWORD sign,easy,less AUTHOR Paul Curtz, May 21 2010 EXTENSIONS New name from Wesley Ivan Hurt, Jun 23 2016 STATUS approved

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Last modified January 29 08:12 EST 2020. Contains 331337 sequences. (Running on oeis4.)