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 A131531 Period 6: repeat [0, 0, 1, 0, 0, -1]. 19
 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also: partial sums of A092220 shifted by two indices. - R. J. Mathar, Feb 08 2008 From Paul Curtz, Jun 05 2011: (Start) The square array of this sequence in the top row and further rows defined as first differences of preceding rows starts (see A167613): .   0,   0,   1,   0,   0,  -1, ... .   0,   1,  -1,   0,  -1,   1, ...  = A092220, .   1,  -2,   1,  -1,   2,  -1, ...  = A131556, .  -3,   3,  -2,   3,  -3    2, ... .   6,  -5,   5,  -6,   5,  -5, ... . -11,  10, -11,  11, -10,  11, ... .  21, -21,  22, -21,  21, -22, ... . -42,  43, -43,  42, -43, -42, ... The main diagonal in this array is A001045; the first super-diagonal is the negated elements of A001045, the second super-diagonal is A078008. The left column of the array is basically the inverse binomial transform, (-1)^n * A024495(n), assuming offset 0. The second column of the array is A131708 with alternating signs, and the third column is A024493 with alternating signs (both assuming offset 0). (End) LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,-1). FORMULA a(n) = (1/6)*((-(n mod 6)+((n+1) mod 6)+((n+3) mod 6)-((n+4) mod 6)). - Paolo P. Lava, Aug 28 2007 G.f.: x^3/(x+1)/(x^2-x+1). - R. J. Mathar, Nov 14 2007 a(n) = (-1)^(n+1)*(((n+1) mod 3) mod 2). - Paolo P. Lava, Mar 14 2011 a(n) = (-A057079(n+1)-(-1)^n)/3. - R. J. Mathar, Jun 13 2011 a(n) = -cos(Pi*(n-1)/3)/3 +sin(Pi*(n-1)/3)/sqrt(3) -(-1)^n/3. - R. J. Mathar, Oct 08 2011 a(n) = ( (-1)^n - (-1)^floor((n+2)/3) )/2. - Bruno Berselli, Jul 09 2013 a(n) + a(n-3) = 0 for n>3. - Wesley Ivan Hurt, Jun 20 2016 MAPLE A131531:=n->[0, 0, 1, 0, 0, -1][(n mod 6)+1]: seq(A131531(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016 MATHEMATICA PadRight[{}, 120, {0, 0, 1, 0, 0, -1}] (* Harvey P. Dale, Nov 11 2012 *) PROG (PARI) a(n)=[0, 0, 1, 0, 0, -1][n%6+1] \\ Charles R Greathouse IV, Jun 01 2011 (MAGMA) &cat[[0, 0, 1, 0, 0, -1]^^20]; // Wesley Ivan Hurt, Jun 20 2016 CROSSREFS Cf. A001045, A024493, A024495, A078008, A092220, A131556, A131708, A167613. Sequence in context: A289035 A276397 A286747 * A022003 A144604 A022926 Adjacent sequences:  A131528 A131529 A131530 * A131532 A131533 A131534 KEYWORD sign,easy AUTHOR Paul Curtz, Aug 26 2007 EXTENSIONS Edited by N. J. A. Sloane, Sep 15 2007 STATUS approved

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Last modified February 23 13:33 EST 2020. Contains 332159 sequences. (Running on oeis4.)