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 A047481 Numbers that are congruent to {0, 2, 5, 7} mod 8. 2
 0, 2, 5, 7, 8, 10, 13, 15, 16, 18, 21, 23, 24, 26, 29, 31, 32, 34, 37, 39, 40, 42, 45, 47, 48, 50, 53, 55, 56, 58, 61, 63, 64, 66, 69, 71, 72, 74, 77, 79, 80, 82, 85, 87, 88, 90, 93, 95, 96, 98, 101, 103, 104, 106, 109, 111, 112, 114, 117, 119, 120, 122, 125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Complement of A047415. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1). FORMULA From Colin Barker, May 14 2012: (Start) a(n) = (1/4+i/4)*((-3+3*i)-i*(-i)^n+i^n+(4-4*i)*n) where i=sqrt(-1). G.f.: x^2*(2+x+x^2)/((1-x)^2*(1+x^2)). (End) a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, May 16 2012 a(n) = (-1*((-1)^((n-1)/2-(-1)^n/4-1/4)))/2+2*(n-1)+1/2. a(n) = cos(n*Pi/2)-1/2*cos((n-1)*Pi/2)-1/2*cos(n*Pi/2)+2*(n-1)+1/2. - Cédric Christian Bernard Gagneux, Mar 05 2014 a(2k) = A047524, a(2k-1) = A047615(k). - Wesley Ivan Hurt, Jun 01 2016 E.g.f.: (2 - sin(x) + cos(x) + (4*x - 3)*exp(x))/2. - Ilya Gutkovskiy, Jun 02 2016 MAPLE A047481:=n->(-1*((-1)^((n-1)/2-(-1)^n/4-1/4)))/2+2*(n-1)+1/2: seq(A047481(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016 MATHEMATICA Select[Range[0, 300], MemberQ[{0, 2, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *) LinearRecurrence[{2, -2, 2, -1}, {0, 2, 5, 7}, 70] (* Harvey P. Dale, May 28 2017 *) PROG (MAGMA) I:=[0, 2, 5, 7, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012 (PARI) a(n)=[-1, 0, 2, 5][n%4]+n\4*8 \\ Charles R Greathouse IV, Mar 05 2014 (PARI) x='x+O('x^100); concat(0, Vec(x^2*(2+x+x^2)/((1-x)^2*(1+x^2)))) \\ Altug Alkan, Dec 24 2015 CROSSREFS Cf. A047415, A047524, A047615. Sequence in context: A268272 A102700 A095371 * A158704 A131854 A005124 Adjacent sequences:  A047478 A047479 A047480 * A047482 A047483 A047484 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 13 05:41 EDT 2021. Contains 344981 sequences. (Running on oeis4.)