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A047285
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Numbers that are congruent to {0, 2, 3, 6} mod 7.
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1
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0, 2, 3, 6, 7, 9, 10, 13, 14, 16, 17, 20, 21, 23, 24, 27, 28, 30, 31, 34, 35, 37, 38, 41, 42, 44, 45, 48, 49, 51, 52, 55, 56, 58, 59, 62, 63, 65, 66, 69, 70, 72, 73, 76, 77, 79, 80, 83, 84, 86, 87, 90, 91, 93, 94, 97, 98, 100, 101, 104, 105, 107, 108, 111
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..64.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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G.f.: x^2*(2+x+3*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n-13+3*i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047276(k), a(2k-1) = A047355(k). (End)
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MAPLE
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A047285:=n->(14*n-13+3*I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n)/8: seq(A047285(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
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MATHEMATICA
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Table[(14n-13+3*I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)
Select[Range[0, 120], MemberQ[{0, 2, 3, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 0, 1, -1}, {0, 2, 3, 6, 7}, 100] (* Harvey P. Dale, Jul 12 2020 *)
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PROG
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(MAGMA) [n : n in [0..150] | n mod 7 in [0, 2, 3, 6]]; // Wesley Ivan Hurt, Jun 02 2016
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CROSSREFS
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Cf. A047276, A047355.
Sequence in context: A285567 A153123 A100913 * A191215 A190847 A201734
Adjacent sequences: A047282 A047283 A047284 * A047286 A047287 A047288
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KEYWORD
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nonn,easy
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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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