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%I #27 Sep 08 2022 08:45:38
%S 1,1,2,4,4,5,7,7,8,10,10,11,13,13,14,16,16,17,19,19,20,22,22,23,25,25,
%T 26,28,28,29,31,31,32,34,34,35,37,37,38,40,40,41,43,43,44,46,46,47,49,
%U 49,50,52,52,53,55,55,56,58,58,59,61,61,62,64,64,65,67,67,68,70,70,71
%N a(n) is congruent to (1,1,2) mod 3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n) = a(n-3)+3 = n-2/3-A131713(n)/3. G.f.: x*(1+x^2+x^3)/((1-x)^2*(1+x+x^2)). [_R. J. Mathar_, Nov 07 2008]
%F a(1)=1, a(2)=1, a(3)=2, a(4)=4, a(n)=a(n-1)+a(n-3)-a(n-4) for n>4. - _Harvey P. Dale_, Dec 09 2012
%F a(n) = (3*n - 2 - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3. - _Wesley Ivan Hurt_, Jul 24 2016
%F a(n) = 1 + floor((n-1)/3) + floor(2*(n-1)/3). - _Wesley Ivan Hurt_, Jul 25 2016
%F a(n) = n - sign((n-1) mod 3). - _Wesley Ivan Hurt_, Sep 25 2017
%p a:=n->add(chrem( [n,j], [1,3] ), j=1..n): seq(a(n)+1, n=-1..70); # _Zerinvary Lajos_, Apr 08 2009
%t LinearRecurrence[{1,0,1,-1},{1,1,2,4},80] (* _Harvey P. Dale_, Dec 09 2012 *)
%o (Magma) I:=[1,1,2]; [n le 3 select I[n] else Self(n-3)+3: n in [1..70]]; // _Vincenzo Librandi_, Jul 25 2016
%Y Cf. A004396 for a(n) congruent to (0, 1, 1) mod 2.
%Y Cf. A131713.
%K easy,nonn
%O 1,3
%A _Giovanni Teofilatto_, Nov 06 2008
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