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Numbers that are congruent to {0, 1, 4, 6, 7} mod 8.
1

%I #19 Sep 08 2022 08:44:57

%S 0,1,4,6,7,8,9,12,14,15,16,17,20,22,23,24,25,28,30,31,32,33,36,38,39,

%T 40,41,44,46,47,48,49,52,54,55,56,57,60,62,63,64,65,68,70,71,72,73,76,

%U 78,79,80,81,84,86,87,88,89,92,94,95,96,97,100,102,103,104

%N Numbers that are congruent to {0, 1, 4, 6, 7} mod 8.

%H G. C. Greubel, <a href="/A047509/b047509.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 + 2*x^2 + 3*x + 1)/(x^6 - x^5 - x + 1). (End)

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

%t Join[{0}, Select[Range[200], MemberQ[{0, 1, 4, 6, 7}, Mod[#, 8]] &]] (* _Vincenzo Librandi_, May 30 2016 *)

%o (Magma) [n: n in [0..200] | n mod 8 in [0,1,4,6,7]]; // _Vincenzo Librandi_, May 30 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_