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%I #20 Sep 08 2022 08:44:57
%S 0,1,2,3,4,8,9,10,11,12,16,17,18,19,20,24,25,26,27,28,32,33,34,35,36,
%T 40,41,42,43,44,48,49,50,51,52,56,57,58,59,60,64,65,66,67,68,72,73,74,
%U 75,76,80,81,82,83,84,88,89,90,91,92,96,97,98,99,100,104
%N Numbers that are congruent to {0, 1, 2, 3, 4} mod 8.
%H Vincenzo Librandi, <a href="/A047453/b047453.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F G.f.: x^2*(1+x+x^2+x^3+4*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F From _Wesley Ivan Hurt_, Jul 31 2016: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
%F a(n) = (40*n - 70 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 12*((n+4) mod 5))/25.
%F a(5k) = 8k-4, a(5k-1) = 8k-5, a(5k-2) = 8k-6, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)
%p A047453:=n->8*floor(n/5)+[(0, 1, 2, 3, 4)][(n mod 5)+1]: seq(A047453(n), n=0..100); # _Wesley Ivan Hurt_, Jul 31 2016
%t Select[Range[0,100], MemberQ[{0, 1, 2, 3, 4}, Mod[#,8]]&] (* or *) LinearRecurrence[{1,0,0,0,1,-1}, {0,1,2,3,4,8}, 80] (* _Harvey P. Dale_, Jul 04 2015 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0..4]]; // _Wesley Ivan Hurt_, Jul 31 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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