A047450 - OEIS

%I #17 Sep 08 2022 08:44:57

%S 0,1,2,3,5,6,8,9,10,11,13,14,16,17,18,19,21,22,24,25,26,27,29,30,32,

%T 33,34,35,37,38,40,41,42,43,45,46,48,49,50,51,53,54,56,57,58,59,61,62,

%U 64,65,66,67,69,70,72,73,74,75,77,78,80,81,82,83,85,86,88

%N Numbers that are congruent to {0, 1, 2, 3, 5, 6} 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*(1+x+x^2+2*x^3+x^4+2*x^5) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - _R. J. Mathar_, Dec 07 2011

%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-33-3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)+6*sin((1+2*n) *Pi/6))/18.

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

%F Sum_{n>=2} (-1)^n/a(n) = 3*(sqrt(2)-1)*Pi/16 + (8-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 26 2021

%p A047450:=n->(24*n-33-3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)+6*sin((1+2*n) *Pi/6))/18: seq(A047450(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016

%t Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)

%o (Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 5, 6]]; // _Wesley Ivan Hurt_, Jun 16 2016

%Y Cf. A047420, A047602.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_