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A047240
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Numbers that are congruent to {0, 1, 2} mod 6.
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10
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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
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OFFSET
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1,3
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COMMENTS
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Partial sums of 0,1,1,4,1,1,4,... - Paul Barry, Feb 19 2007
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
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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 Deléham, Oct 22 2011.
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MATHEMATICA
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Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 2 &] (* From Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
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PROG
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(MAGMA) [0], [6*Floor(n/3) + (n mod 3): n in [1..65]]; // Vincenzo Librandi, Oct 23 2011
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CROSSREFS
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Cf. A047234, A047242.
Sequence in context: A190212 A031198 A201819 * A080333 A194369 A039592
Adjacent sequences: A047237 A047238 A047239 * A047241 A047242 A047243
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Paul Barry, Feb 19 2007
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STATUS
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approved
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