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A010761 a(n) = floor(n/2) + floor(n/3).

%I A010761 #28 Mar 30 2023 02:37:02
%S A010761 0,1,2,3,3,5,5,6,7,8,8,10,10,11,12,13,13,15,15,16,17,18,18,20,20,21,
%T A010761 22,23,23,25,25,26,27,28,28,30,30,31,32,33,33,35,35,36,37,38,38,40,40,
%U A010761 41,42,43,43,45,45,46,47,48,48,50,50,51,52,53,53,55,55,56,57,58,58,60,60
%N A010761 a(n) = floor(n/2) + floor(n/3).
%H A010761 Vincenzo Librandi, <a href="/A010761/b010761.txt">Table of n, a(n) for n = 1..2000</a>
%H A010761 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F A010761 a(n) = A004526(n) + A002264(n). - _Reinhard Zumkeller_, Jul 25 2005
%F A010761 From _Michael Somos_, Aug 07 2005: (Start)
%F A010761 G.f.: x^2*(1+2*x+2*x^2)/((1-x^2)*(1-x^3)).
%F A010761 a(-n) = -2-a(n-1). (End)
%F A010761 a(n) = a(n-2)+a(n-3)-a(n-5). - _Wesley Ivan Hurt_, Jan 27 2022
%F A010761 Sum_{n>=2} (-1)^n/a(n) = sqrt(2*(1-1/sqrt(5)))*Pi/10 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - _Amiram Eldar_, Mar 30 2023
%p A010761 seq(floor(n/2) + floor(n/3), n=1..64);
%t A010761 Table[Floor[n/2] + Floor[n/3], {n, 100}] (* _Wesley Ivan Hurt_, Feb 21 2014 *)
%t A010761 LinearRecurrence[{0,1,1,0,-1},{0,1,2,3,3},80] (* _Harvey P. Dale_, May 05 2018 *)
%o A010761 (PARI) a(n)=n\2+n\3
%o A010761 (Magma) [Floor (n/2)+Floor(n/3): n in [0..100]]; // _Vincenzo Librandi_, Feb 22 2014
%Y A010761 Cf. A001622, A010762, A110532.
%Y A010761 Cf. A002264, A004526.
%K A010761 nonn,easy
%O A010761 1,3
%A A010761 _Simon Plouffe_