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%I #17 Sep 08 2022 08:44:57
%S 1,2,4,5,6,9,10,12,13,14,17,18,20,21,22,25,26,28,29,30,33,34,36,37,38,
%T 41,42,44,45,46,49,50,52,53,54,57,58,60,61,62,65,66,68,69,70,73,74,76,
%U 77,78,81,82,84,85,86,89,90,92,93,94,97,98,100,101,102
%N Numbers that are congruent to {1, 2, 4, 5, 6} mod 8.
%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*(1+x)*(x^2-x+1)*(2*x^2+x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%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 - 30 + 3*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) - 7*((n+4) mod 5))/25.
%F a(5k) = 8k-2, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-7. (End)
%p A047435:=n->8*floor(n/5)+[(1, 2, 4, 5, 6)][(n mod 5)+1]: seq(A047435(n), n=0..100); # _Wesley Ivan Hurt_, Aug 01 2016
%t Select[Range[0, 100], MemberQ[{1, 2, 4, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Aug 01 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [1, 2, 4, 5, 6]]; // _Wesley Ivan Hurt_, Aug 01 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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