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%I #21 Sep 08 2022 08:45:03
%S 1,0,3,4,3,6,7,6,9,10,9,12,13,12,15,16,15,18,19,18,21,22,21,24,25,24,
%T 27,28,27,30,31,30,33,34,33,36,37,36,39,40,39,42,43,42,45,46,45,48,49,
%U 48,51,52,51,54,55,54,57,58,57,60,61,60,63,64,63,66,67,66,69,70,69,72
%N a(n) = n + (-1)^(n mod 3).
%C The arithmetic function v_3(n,3) as defined in A289187. - _Robert Price_, Aug 22 2017
%H Harry J. Smith, <a href="/A061800/b061800.txt">Table of n, a(n) for n=0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F O.g.f.: (1-x+3*x^2)/((-1+x)^2*(1+x+x^2)). - _R. J. Mathar_, Apr 02 2008
%F a(n) = (3*n + 1 - 4*cos(2*(n+2)*Pi/3))/3. - _Wesley Ivan Hurt_, Sep 26 2017
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3. - _Wesley Ivan Hurt_, Oct 07 2017
%e a(4) = 4 + (-1)^1 = 3.
%p A061800:=n->n+(-1)^(n mod 3): seq(A061800(n), n=0..150); # _Wesley Ivan Hurt_, Oct 07 2017
%t Table[n + (-1)^Mod[n, 3], {n, 0, 80}] (* _Vincenzo Librandi_, Aug 23 2017 *)
%o (PARI) { for (n=0, 1000, write("b061800.txt", n, " ", n + (-1)^(n%3)) ) } \\ _Harry J. Smith_, Jul 28 2009
%o (Magma) [n+(-1)^(n mod 3): n in [0..80]]; // _Vincenzo Librandi_, Aug 23 2017
%Y Cf. A004442, A014681, A289187.
%K easy,nonn
%O 0,3
%A _Olivier Gérard_, Jun 22 2001
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