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A047408 Numbers that are congruent to {1, 4, 6} mod 8.

%I A047408 #27 Oct 14 2024 00:04:00
%S A047408 1,4,6,9,12,14,17,20,22,25,28,30,33,36,38,41,44,46,49,52,54,57,60,62,
%T A047408 65,68,70,73,76,78,81,84,86,89,92,94,97,100,102,105,108,110,113,116,
%U A047408 118,121,124,126,129,132,134,137,140,142,145,148,150,153,156,158
%N A047408 Numbers that are congruent to {1, 4, 6} mod 8.
%H A047408 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047408 G.f.: x*(1+3*x+2*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 05 2011
%F A047408 a(n) = 3n - 2 - floor(n/3). - _Wesley Ivan Hurt_, Nov 07 2013
%F A047408 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047408 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047408 a(n) = (24*n-15-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
%F A047408 a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-7. (End)
%F A047408 E.g.f.: 2 + exp(x)*(8*x - 5)/3 - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Mar 30 2023
%p A047408 A047408:=n->3*n-floor(n/3)-2; seq(A047408(k), k=1..100); # _Wesley Ivan Hurt_, Nov 07 2013
%t A047408 Table[3n-Floor[n/3]-2, {n, 100}] (* _Wesley Ivan Hurt_, Nov 07 2013 *)
%o A047408 (Magma) [n : n in [0..150] | n mod 8 in [1, 4, 6]]; // _Wesley Ivan Hurt_, Jun 10 2016
%Y A047408 Cf. A047622.
%K A047408 nonn,easy
%O A047408 1,2
%A A047408 _N. J. A. Sloane_