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%I #20 Sep 08 2022 08:44:57
%S 0,1,2,3,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,24,25,26,27,29,
%T 30,31,32,33,34,35,37,38,39,40,41,42,43,45,46,47,48,49,50,51,53,54,55,
%U 56,57,58,59,61,62,63,64,65,66,67,69,70,71,72,73,74,75,77,78,79,80,81
%N Numbers that are congruent to {0, 1, 2, 3, 5, 6, 7} mod 8.
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F G.f.: x*(1-x^4)*(1-x^6)/((1-x)^2*(1-x^3)*(1-x^7)) = x*(1+x+x^2+x^3)*(1+x^3)/((1-x)*(1-x^7)).
%F a(n) = a(n-7) + 8 = -a(-n) for n > 7.
%F From _Wesley Ivan Hurt_, Jul 21 2016: (Start)
%F a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F a(n) = (56*n - 56 + (n mod 7) + ((n+1) mod 7) - 6*((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.
%F a(7*k) = 8*k-1, a(7*k-1) = 8*k-2, a(7*k-2) = 8*k-3, a(7*k-3) = 8*k-5, a(7*k-4) = 8*k-6, a(7*k-5) = 8*k-7, a(7*k-6) = 8*k-8. (End)
%p A047588:=n->8*floor(n/7)+[0, 1, 2, 3, 5, 6, 7][(n mod 7)+1]: seq(A047588(n), n=0..100); # _Wesley Ivan Hurt_, Jul 21 2016
%t Complement[Range[100],4Range[1,99,2]] (* _Harvey P. Dale_, Jan 29 2011 *)
%o (PARI) a(n)=n+1+(n-4)\7
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 3, 5, 6, 7]]; // _Wesley Ivan Hurt_, Jul 21 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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