%I #22 Sep 08 2022 08:44:57

%S 0,4,5,6,7,8,12,13,14,15,16,20,21,22,23,24,28,29,30,31,32,36,37,38,39,

%T 40,44,45,46,47,48,52,53,54,55,56,60,61,62,63,64,68,69,70,71,72,76,77,

%U 78,79,80,84,85,86,87,88,92,93,94,95,96,100,101,102,103

%N Numbers that are congruent to {0, 4, 5, 6, 7} mod 8.

%H G. C. Greubel, <a href="/A047567/b047567.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 From _Chai Wah Wu_, May 30 2016: (Start)

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

%F G.f.: x^2*(x^4 + x^3 + x^2 + x + 4)/(x^6 - x^5 - x + 1). (End)

%F From _Wesley Ivan Hurt_, Aug 16 2016: (Start)

%F a(n) = a(n-5) + 8 for n > 5.

%F a(n) = n + 2 + 3*floor((n-2)/5).

%F a(n) = (8*n + 4 - 3*((n+3) mod 5))/5.

%F a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-3, a(5k-3) = 8k-4, a(5k-4) = 8k-8. (End)

%p A047567:=n->8*floor(n/5)+[0, 4, 5, 6, 7][(n mod 5)+1]: seq(A047567(n), n=0..100); # _Wesley Ivan Hurt_, Aug 16 2016

%t Select[Range[0,100], MemberQ[{0,4,5,6,7}, Mod[#,8]]&] (* _Harvey P. Dale_, Apr 16 2014 *)

%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 4, 5, 6, 7, 8}, 50] (* _G. C. Greubel_, May 30 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5, 6, 7]]; // _Wesley Ivan Hurt_, Aug 16 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_