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A047467
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Numbers that are congruent to {0, 2} mod 8.
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13
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0, 2, 8, 10, 16, 18, 24, 26, 32, 34, 40, 42, 48, 50, 56, 58, 64, 66, 72, 74, 80, 82, 88, 90, 96, 98, 104, 106, 112, 114, 120, 122, 128, 130, 136, 138, 144, 146, 152, 154, 160, 162, 168, 170, 176, 178, 184, 186, 192, 194, 200, 202, 208, 210, 216, 218, 224, 226, 232
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OFFSET
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1,2
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LINKS
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David Lovler, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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From R. J. Mathar, Sep 19 2008: (Start)
a(n) = 4*n - 5 - (-1)^n = 2*A042948(n-1).
G.f.: 2*x^2*(1+3x)/((1-x)^2*(1+x)). (End)
a(n) = 8*n - a(n-1) - 14 with a(1)=0. - Vincenzo Librandi, Aug 06 2010
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=2 and b(k)=2^(k+2)for k > 0. - Philippe Deléham, Oct 17 2011
a(n) = floor((8/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012
Sum_{n>=2} (-1)^n/a(n) = Pi/16 + 3*log(2)/8. - Amiram Eldar, Dec 18 2021
E.g.f.: 6 + (4*x - 5)*exp(x) - exp(-x). - David Lovler, Jul 22 2022
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MATHEMATICA
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{#, #+2}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 8}, 60] (* Harvey P. Dale, Nov 30 2019 *)
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PROG
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(PARI) forstep(n=0, 200, [2, 6], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = 4*n - 5 - (-1)^n; \\ David Lovler, Jul 25 2022
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CROSSREFS
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Union of A008590 and A017089.
Cf. A030308, A042948.
Sequence in context: A329952 A073886 A079930 * A079599 A126002 A110913
Adjacent sequences: A047464 A047465 A047466 * A047468 A047469 A047470
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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 Vincenzo Librandi, Aug 06 2010
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STATUS
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approved
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