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A130823 Each odd number appears thrice.

%I A130823 #44 May 07 2025 20:06:08
%S A130823 1,1,1,3,3,3,5,5,5,7,7,7,9,9,9,11,11,11,13,13,13,15,15,15,17,17,17,19,
%T A130823 19,19,21,21,21,23,23,23,25,25,25,27,27,27,29,29,29,31,31,31,33,33,33,
%U A130823 35,35,35,37,37,37,39,39,39,41,41,41,43,43,43,45,45,45,47,47,47,49,49
%N A130823 Each odd number appears thrice.
%C A130823 Partial sums of 1,0,0,2,0,0,2,0,0,2,0,0,... . - _Emeric Deutsch_, Jul 23 2007
%H A130823 Vincenzo Librandi, <a href="/A130823/b130823.txt">Table of n, a(n) for n = 1..10000</a>
%H A130823 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A130823 a(n) = 2*floor((n-1)/3) + 1. - _Joerg Arndt_, Jan 02 2024 [corrected by _Aadesh Tikhe_, 06 May 2025]
%F A130823 G.f.: x*(1 + x^3)/((1 - x)*(1 - x^3)). - _Emeric Deutsch_, Jul 23 2007
%F A130823 From _Michael Somos_, Aug 16 2007: (Start)
%F A130823 Euler transform of length 6 sequence [1, 0, 2, 0, 0, -1].
%F A130823 a(n + 3) = a(n) + 2.
%F A130823 a(n) = - a(1-n) for all n in Z. (End)
%F A130823 a(n) = floor((n-1)*(n+1)/3) - floor((n-2)*n/3). - _Bruno Berselli_, Mar 03 2017
%F A130823 a(n) = (6*n-3-4*sqrt(3)*sin(2*(n-2)*Pi/3))/9. - _Wesley Ivan Hurt_, Sep 30 2017
%e A130823 G.f. = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 3*x^6 + 5*x^7 + 5*x^8 + 5*x^9 + 7*x^10 + ...
%p A130823 G:=x*(1+x^3)/((1-x)*(1-x^3)): Gser:=series(G,x=0,82): seq(coeff(Gser,x,n),n= 1..75); # _Emeric Deutsch_, Jul 23 2007
%t A130823 Flatten[Table[n,{n,1,49,2},{3}]] (* or *) LinearRecurrence[{1,0,1,-1},{1,1,1,3},100] (* or *) Accumulate[PadRight[{1},100,{2,0,0}]] (* _Harvey P. Dale_, Apr 20 2015 *)
%o A130823 (PARI) {a(n) = (n-1)\3*2+1}; \\ _Michael Somos_, Aug 16 2007
%o A130823 (Magma) [Floor((n-1)/3)*2+1: n in [1..80]]; // _Vincenzo Librandi_, Aug 10 2011
%K A130823 nonn,easy
%O A130823 1,4
%A A130823 _Paul Curtz_, Jul 17 2007
%E A130823 More terms from _Emeric Deutsch_, Jul 23 2007