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

%S 0,1,2,4,7,8,9,10,12,15,16,17,18,20,23,24,25,26,28,31,32,33,34,36,39,

%T 40,41,42,44,47,48,49,50,52,55,56,57,58,60,63,64,65,66,68,71,72,73,74,

%U 76,79,80,81,82,84,87,88,89,90,92,95,96,97,98,100,103,104

%N Numbers that are congruent to {0, 1, 2, 4, 7} 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 From _Chai Wah Wu_, Jun 10 2016: (Start)

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

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

%F From _Wesley Ivan Hurt_, Jul 28 2016: (Start)

%F a(n) = a(n-5) + 8 for n > 5.

%F a(n) = (40*n - 50 - 7*(n mod 5) - 2*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

%F a(5k) = 8k-1, a(5k-1) = 8k-4, a(5k-2) = 8k-6, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)

%p A047542:=n->8*floor(n/5)+[(0, 1, 2, 4, 7)][(n mod 5)+1]: seq(A047542(n), n=0..100); # _Wesley Ivan Hurt_, Jul 28 2016

%t Select[Range[0, 100], MemberQ[{0, 1, 2, 4, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 28 2016 *)

%t LinearRecurrence[{1,0,0,0,1,-1},{0,1,2,4,7,8},80] (* _Harvey P. Dale_, Jan 27 2021 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 4, 7]]; // _Wesley Ivan Hurt_, Jul 28 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_