A047503 - OEIS

%I #19 Dec 25 2023 14:41:00

%S 0,2,3,4,5,7,8,10,11,12,13,15,16,18,19,20,21,23,24,26,27,28,29,31,32,

%T 34,35,36,37,39,40,42,43,44,45,47,48,50,51,52,53,55,56,58,59,60,61,63,

%U 64,66,67,68,69,71,72,74,75,76,77,79,80,82,83,84,85,87

%N Numbers that are congruent to {0, 2, 3, 4, 5, 7} mod 8.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).

%F G.f.: x^2*(2+x+x^2+x^3+2*x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015

%F From _Wesley Ivan Hurt_, Jun 16 2016: (Start)

%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

%F a(n) = (24*n-21+3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)-6*sin((1-2*n)*Pi/6))/18.

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

%F Sum_{n>=2} (-1)^n/a(n) = log(2)/8 - sqrt(2)*Pi/16 - sqrt(2)*log(99-70*sqrt(2))/16. - _Amiram Eldar_, Dec 27 2021

%p A047503:=n->(24*n-21+3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)-6*sin((1-2*n)*Pi/6))/18: seq(A047503(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016

%t Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)

%t LinearRecurrence[{1,0,0,0,0,1,-1},{0,2,3,4,5,7,8},100] (* _Harvey P. Dale_, Dec 25 2023 *)

%o (Magma) [n : n in [0..100] | n mod 8 in [0, 2, 3, 4, 5, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016

%Y Cf. A047424, A047587.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_