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 A047240 Numbers that are congruent to {0, 1, 2} mod 6. 10
 0, 1, 2, 6, 7, 8, 12, 13, 14, 18, 19, 20, 24, 25, 26, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 72, 73, 74, 78, 79, 80, 84, 85, 86, 90, 91, 92, 96, 97, 98, 102, 103, 104, 108, 109, 110, 114, 115, 116, 120, 121, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Partial sums of 0,1,1,4,1,1,4,... - Paul Barry, Feb 19 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 FORMULA G.f.: x(1+x+4x^2)/((1-x)(1-x^3)); a(n)=cos(2*pi*n/3)+sqrt(3)*sin(2*pi*n/3)/3+2n-1; - Paul Barry, Feb 19 2007 a(n)=n-1 + 3*floor((n-1)/3) . [From Philippe DELEHAM, Apr 21 2009] a(n)=6*floor(n/3) + (n mod 3) [From Gary Detlefs, Mar 09 2010] a(n+1)=sum_k>=0 {A030341(n,k)*b(k)} with b(0)=1 and b(k)=2*3^k for k>0. - From Philippe DelĂ©ham, Oct 22 2011. MATHEMATICA Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 2 &] (* From Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *) PROG (MAGMA) [0], [6*Floor(n/3) + (n mod 3): n in [1..65]]; // Vincenzo Librandi, Oct 23 2011 CROSSREFS Cf. A047234, A047242. Sequence in context: A190212 A031198 A201819 * A080333 A194369 A039592 Adjacent sequences:  A047237 A047238 A047239 * A047241 A047242 A047243 KEYWORD nonn AUTHOR EXTENSIONS More terms from Paul Barry, Feb 19 2007 STATUS approved

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