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Numbers that are congruent to {0, 1, 3, 4, 5} mod 8.
1

%I #15 Sep 08 2022 08:44:57

%S 0,1,3,4,5,8,9,11,12,13,16,17,19,20,21,24,25,27,28,29,32,33,35,36,37,

%T 40,41,43,44,45,48,49,51,52,53,56,57,59,60,61,64,65,67,68,69,72,73,75,

%U 76,77,80,81,83,84,85,88,89

%N Numbers that are congruent to {0, 1, 3, 4, 5} mod 8.

%H G. C. Greubel, <a href="/A047601/b047601.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 29 2016: (Start)

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

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

%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 8}, 50] (* _G. C. Greubel_, May 29 2016 *)

%o (Magma) [n : n in [0..100] | n mod 8 in [0, 1, 3, 4, 5]]; // _Wesley Ivan Hurt_, May 29 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_