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%I #18 Sep 08 2022 08:44:57
%S 3,4,5,6,7,11,12,13,14,15,19,20,21,22,23,27,28,29,30,31,35,36,37,38,
%T 39,43,44,45,46,47,51,52,53,54,55,59,60,61,62,63,67,68,69,70,71,75,76,
%U 77,78,79,83,84,85,86,87,91,92,93,94,95,99,100,101,102,103
%N Numbers that are congruent to {3, 4, 5, 6, 7} mod 8.
%H G. C. Greubel, <a href="/A047562/b047562.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*(x^5 + x^4 + x^3 + x^2 + x + 3)/(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-1)/5).
%F a(n) = (8*n + 7 - 3*((n+4) 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-5. (End)
%p A047562:=n->8*floor(n/5)+[3, 4, 5, 6, 7][(n mod 5)+1]: seq(A047562(n), n=0..100); # _Wesley Ivan Hurt_, Aug 16 2016
%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {3, 4, 5, 6, 7, 11}, 50] (* _G. C. Greubel_, May 29 2016 *)
%t #+{3,4,5,6,7}&/@(8*Range[0,20])//Flatten (* _Harvey P. Dale_, May 25 2020 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 6, 7]]; // _Wesley Ivan Hurt_, Aug 16 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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