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 A047615 Numbers that are congruent to {0, 5} mod 8. 15
 0, 5, 8, 13, 16, 21, 24, 29, 32, 37, 40, 45, 48, 53, 56, 61, 64, 69, 72, 77, 80, 85, 88, 93, 96, 101, 104, 109, 112, 117, 120, 125, 128, 133, 136, 141, 144, 149, 152, 157, 160, 165, 168, 173, 176, 181, 184, 189, 192, 197, 200, 205, 208, 213, 216, 221, 224, 229, 232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = 8*n-a(n-1)-11 (with a(1)=0). - Vincenzo Librandi, Aug 06 2010 a(n+1) = Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=5 and b(k)=2^(k+2) for k>0. - Philippe Deléham, Oct 17 2011 From Wesley Ivan Hurt, Mar 26 2015: (Start) a(n) = a(n-1)+a(n-2)-a(n-3). a(n) = (8n - 7 + (-1)^n)/2. (End) G.f.: x^2*(5+3*x) / ((1-x)^2*(1+x)). - Colin Barker, Aug 25 2016 From Franck Maminirina Ramaharo, Jul 23 2018: (Start) a(n) = A047470(n) - (-1)^(n - 1) + 1. E.g.f.: (6 + exp(-x) + (8*x - 7)*exp(x))/2. (End) MAPLE a:=n->add(4-(-1)^j, j=1..n): seq(a(n), n=0..59); # Zerinvary Lajos, Dec 13 2008 MATHEMATICA Table[(8 n - 7 + (-1)^n)/2, {n, 1, 40}] (* Wesley Ivan Hurt, Mar 26 2015 *) Rest@ CoefficientList[Series[x^2*(5 + 3 x)/((1 - x)^2*(1 + x)), {x, 0, 59}], x] (* Michael De Vlieger, Aug 25 2016 *) Rest@(Range[0, 60]! CoefficientList[ Series[(6 + Exp[-x] + (8 x - 7)*Exp[x])/2, {x, 0, 60}], x]) (* or *) LinearRecurrence[{1, 1, -1}, {0, 5, 8}, 60] (* Robert G. Wilson v, Jul 23 2018 *) PROG (PARI) forstep(n=0, 200, [5, 3], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011 (MAGMA) [(8*n - 7 + (-1)^n)/2 : n in [1..50]]; // Wesley Ivan Hurt, Mar 26 2015 (PARI) concat(0, Vec(x^2*(5+3*x)/((1-x)^2*(1+x)) + O(x^100))) \\ Colin Barker, Aug 25 2016 (GAP) Filtered([0..250], n->n mod 8=0 or n mod 8=5); # Muniru A Asiru, Jul 23 2018 CROSSREFS Cf. A047398, A047452, A047461, A047470, A047524, A047535, A047617. Sequence in context: A030606 A090661 A214976 * A314421 A314422 A140488 Adjacent sequences:  A047612 A047613 A047614 * A047616 A047617 A047618 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Aug 06 2010 STATUS approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)