A047400 - OEIS

%I #29 Dec 25 2023 13:45:43

%S 1,3,6,9,11,14,17,19,22,25,27,30,33,35,38,41,43,46,49,51,54,57,59,62,

%T 65,67,70,73,75,78,81,83,86,89,91,94,97,99,102,105,107,110,113,115,

%U 118,121,123,126,129,131,134,137,139,142,145,147,150,153,155,158

%N Numbers that are congruent to {1, 3, 6} mod 8.

%C Union of A017077, A017101 and A017137. - _R. J. Mathar_, Apr 14 2008

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F a(n) = A004773(n-1) + A004773(n). - _Gary W. Adamson_, Sep 13 2007

%F G.f.: x*(1+x)*(2x^2+x+1)/((-1+x)^2*(x^2+x+1)). a(n) = a(n-3)+8 for n>3. - _R. J. Mathar_, Apr 14 2008

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F a(n) = 2*(12*n-9+sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047400:=n->2*(12*n-9+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047400(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)

%o (PARI) a(n) = {x=8*floor((n-1)/3);if(n%3==1,x=x+1);if(n%3==2,x=x+3);if(n%3==0,x=x+6);x} \\ _Michael B. Porter_, Oct 02 2009

%o (Magma) [n: n in [1..300] | n mod 8 in [1, 3, 6]]; // _Vincenzo Librandi_, Mar 27 2011

%Y Cf. A004773.

%Y Cf. A017077, A017101, A017137.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_