A047559 - OEIS

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

%S 0,1,3,6,7,8,9,11,14,15,16,17,19,22,23,24,25,27,30,31,32,33,35,38,39,

%T 40,41,43,46,47,48,49,51,54,55,56,57,59,62,63,64,65,67,70,71,72,73,75,

%U 78,79,80,81,83,86,87,88,89,91,94,95,96,97,99,102,103,104

%N Numbers that are congruent to {0, 1, 3, 6, 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 a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=7, a(5)=8, a(n) = a(n-1) + a(n-5) - a(n-6) for n>6. - _Harvey P. Dale_, Mar 04 2015

%F From _Wesley Ivan Hurt_, Jul 25 2016: (Start)

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

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

%F a(n) = (40*n - 35 + 3*(n mod 5) - 7*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

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

%p A047559:=n->8*floor(n/5)+[0, 1, 3, 6, 7][(n mod 5)+1]: seq(A047559(n), n=0..100); # _Wesley Ivan Hurt_, Jul 25 2016

%t Select[Range[0,100], MemberQ[{0,1,3,6,7}, Mod[#,8]]&] (* or *) LinearRecurrence[{1,0,0,0,1,-1}, {0,1,3,6,7,8}, 80] (* _Harvey P. Dale_, Mar 04 2015 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 6, 7]]; // _Wesley Ivan Hurt_, Jul 25 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_