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%I A047496 #19 Sep 08 2022 08:44:57
%S A047496 0,2,4,5,7,8,10,12,13,15,16,18,20,21,23,24,26,28,29,31,32,34,36,37,39,
%T A047496 40,42,44,45,47,48,50,52,53,55,56,58,60,61,63,64,66,68,69,71,72,74,76,
%U A047496 77,79,80,82,84,85,87,88,90,92,93,95,96,98,100,101,103
%N A047496 Numbers that are congruent to {0, 2, 4, 5, 7} mod 8.
%H A047496 Vincenzo Librandi, <a href="/A047496/b047496.txt">Table of n, a(n) for n = 1..1000</a>
%H A047496 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A047496 G.f.: x^2*(x + 1)*(x^3 + x^2 + 2)/((x-1)^2*(x^4+x^3+x^2+x+1)). [_Colin Barker_, Jun 22 2012]
%F A047496 From _Wesley Ivan Hurt_, Jul 31 2016: (Start)
%F A047496 a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
%F A047496 a(n) = (40*n - 30 - 2*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((n+3) mod 5) + 3*((n+4) mod 5))/25.
%F A047496 a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)
%p A047496 A047496:=n->8*floor(n/5)+[(0, 2, 4, 5, 7)][(n mod 5)+1]: seq(A047496(n), n=0..100); # _Wesley Ivan Hurt_, Jul 31 2016
%t A047496 Select[Range[0, 100], MemberQ[{0, 2, 4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 31 2016 *)
%o A047496 (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 5, 7]]; // _Wesley Ivan Hurt_, Jul 31 2016
%K A047496 nonn,easy
%O A047496 1,2
%A A047496 _N. J. A. Sloane_

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