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A047238
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Numbers that are congruent to {0, 2} mod 6.
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3
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0, 2, 6, 8, 12, 14, 18, 20, 24, 26, 30, 32, 36, 38, 42, 44, 48, 50, 54, 56, 60, 62, 66, 68, 72, 74, 78, 80, 84, 86, 90, 92, 96, 98, 102, 104, 108, 110, 114, 116, 120, 122, 126, 128, 132, 134, 138, 140, 144, 146, 150
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OFFSET
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1,2
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LINKS
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B. Berselli, Table of n, a(n) for n = 1..10000.
Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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Contribution from Bruno Berselli, Jun 24 2010: (Start)
G.f.: 2*x*(1+2*x)/((1+x)*(1-x)^2).
a(n) = a(n-1) +a(n-2) -a(n-3), a(0)=0, a(1)=2, a(2)=6.
a(n) = (6*n-(-1)^n-7)/2.
a(n) = 2*A032766(n-1). (End)
a(n)=6*n-a(n-1)-10 (with a(1)=0) [From Vincenzo Librandi, Aug 05 2010]
a(n+1)=Sum_k>=0 {A030308(n,k)*A111286(k+2)}. - From Philippe Deléham, Oct 17 2011.
a(n) = 2*floor(3*n/2). - Enrique Pérez Herrero, Jul 04 2012
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EXAMPLE
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For n=2, a(2)=6*2-0-10=2; n=3, a(3)=6*3-2-10=6; n=4, a(4)=6*4-6-10=8 [From Vincenzo Librandi, Aug 05 2010]
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MATHEMATICA
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Select[Range[0, 200], MemberQ[{0, 2}, Mod[#, 6]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {0, 2, 6}, 70] (* From Harvey P. Dale, June 15 2011 *)
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PROG
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(PARI) forstep(n=0, 200, [2, 4], print1(n", "))) \\ Charles R Greathouse IV, Oct 17 2011
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CROSSREFS
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Cf. A047270 [(6*n-(-1)^n-1)/2], A047235 [(6*n-(-1)^n-3)/2], A047241 [(6*n-(-1)^n-5)/2].
Sequence in context: A064212 A056906 A209249 * A189933 A213638 A191965
Adjacent sequences: A047235 A047236 A047237 * A047239 A047240 A047241
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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