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A242112 a(n) = floor((2*n+6)/(5-(-1)^n)).

%I A242112 #36 Feb 09 2024 12:49:06
%S A242112 1,1,2,2,3,2,4,3,5,4,6,4,7,5,8,6,9,6,10,7,11,8,12,8,13,9,14,10,15,10,
%T A242112 16,11,17,12,18,12,19,13,20,14,21,14,22,15,23,16,24,16,25,17,26,18,27,
%U A242112 18,28,19,29,20,30,20,31,21,32,22,33,22,34,23,35,24,36
%N A242112 a(n) = floor((2*n+6)/(5-(-1)^n)).
%H A242112 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,0,-1).
%F A242112 a(n) = a(n-2) + a(n-6) - a(n-8).
%F A242112 a(n) = ( n+3 - A093718(n) ) / A010693(n).
%F A242112 From _Robert Israel_, Aug 22 2014: (Start)
%F A242112 a(n) = sqrt(3)/18*(sin(2*n*Pi/3)+sin(n*Pi/3)) + 1/6*(cos(2*n*Pi/3)-cos(n*Pi/3)) + (-1)^n*(2+n)/12 + 5*(n+2)/12.
%F A242112 G.f.: (1 + x + x^2 + x^3 + x^4)/(1 - x^2 - x^6 + x^8). (End)
%F A242112 a(n) = 1 + n/2 if n is even, otherwise a(n) = 1 + floor(n/3). - _Bruno Berselli_, Aug 22 2014
%p A242112 A242112:=n->floor((2*n+6)/(5-(-1)^n)): seq(A242112(n), n=0..100);
%t A242112 Table[Floor[(2 n + 6)/(5 - (-1)^n)], {n, 0, 100}]
%t A242112 LinearRecurrence[{0,1,0,0,0,1,0,-1},{1,1,2,2,3,2,4,3},80] (* _Harvey P. Dale_, Oct 24 2017 *)
%o A242112 (Magma) [Floor((2*n+6)/(5-(-1)^n)) : n in [0..100]];
%o A242112 (Magma) [IsEven(n) select 1+n/2 else 1+Floor(n/3): n in [0..80]]; // _Bruno Berselli_, Aug 22 2014
%Y A242112 Cf. A010693, A093718.
%K A242112 nonn,easy
%O A242112 0,3
%A A242112 _Wesley Ivan Hurt_, Aug 21 2014