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A047578
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Numbers that are congruent to {2, 5, 6, 7} mod 8.
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4
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2, 5, 6, 7, 10, 13, 14, 15, 18, 21, 22, 23, 26, 29, 30, 31, 34, 37, 38, 39, 42, 45, 46, 47, 50, 53, 54, 55, 58, 61, 62, 63, 66, 69, 70, 71, 74, 77, 78, 79, 82, 85, 86, 87, 90, 93, 94, 95, 98, 101, 102, 103, 106, 109, 110, 111, 114, 117, 118, 119, 122, 125
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..62.
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
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FORMULA
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G.f.: x*(1+x)*(x^2-x+2) / ((1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
a(n) = 2*n - cos(Pi*n/2). - Wesley Ivan Hurt, Oct 22 2013
From Wesley Ivan Hurt, May 20 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n > 4.
a(n) = (4*n - i^(-n) - i^n)/2 where i=sqrt(-1).
a(2n) = A047550(n), a(2n-1) = A016825(n-1). (End)
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MAPLE
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A047578:=n->2*n-cos(Pi*n/2): seq(A047578(n), n=1..100); # Wesley Ivan Hurt, Oct 22 2013
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MATHEMATICA
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Flatten[#+{2, 5, 6, 7}&/@(8Range[0, 20])] (* Harvey P. Dale, Jan 26 2011 *)
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PROG
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(Sage) [lucas_number1(n, 0, 1)+2*n+2 for n in range(0, 56)] # Zerinvary Lajos, Jul 06 2008
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CROSSREFS
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Cf. A016825, A047404, A047431, A047546, A047550, A056594.
Sequence in context: A285032 A002157 A050002 * A259605 A284393 A287366
Adjacent sequences: A047575 A047576 A047577 * A047579 A047580 A047581
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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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EXTENSIONS
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More terms from Wesley Ivan Hurt, May 20 2016
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STATUS
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approved
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