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 A047467 Numbers that are congruent to {0, 2} mod 8. 13
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS David Lovler, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA 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 MATHEMATICA {#, #+2}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 8}, 60] (* Harvey P. Dale, Nov 30 2019 *) PROG (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 CROSSREFS 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 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Aug 06 2010 STATUS approved

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Last modified March 22 02:41 EDT 2023. Contains 361413 sequences. (Running on oeis4.)