login
a(n) = floor(n/2) + floor(3*n/4).
1

%I #39 Jan 31 2023 15:11:18

%S 0,0,2,3,5,5,7,8,10,10,12,13,15,15,17,18,20,20,22,23,25,25,27,28,30,

%T 30,32,33,35,35,37,38,40,40,42,43,45,45,47,48,50,50,52,53,55,55,57,58,

%U 60,60,62,63,65,65,67,68,70,70,72,73,75,75,77,78,80,80,82,83,85,85,87,88,90,90,92,93,95,95,97

%N a(n) = floor(n/2) + floor(3*n/4).

%C List of quadruples [5*k, 5*k, 5*k+2, 5*k+3]. - _Luce ETIENNE_, Aug 14 2017

%H Colin Barker, <a href="/A187322/b187322.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F a(n) = A004526(n) + A057353(n). - _Michel Marcus_, Aug 14 2017

%F a(n) = (10*n-5+3*cos(n*Pi)+2*(cos(n*Pi/2)-sin(n*Pi/2)))/8. - _Luce ETIENNE_, Aug 14 2017

%F From _Colin Barker_, Aug 14 2017: (Start)

%F G.f.: x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)).

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>4.

%F (End)

%t Table[Floor[n/2]+Floor[3n/4], {n,0,120}]

%t LinearRecurrence[{1,0,0,1,-1},{0,0,2,3,5},80] (* _Harvey P. Dale_, Dec 05 2018 *)

%o (PARI) a(n) = n\2 + 3*n\4; \\ _Altug Alkan_, Aug 14 2017

%o (PARI) concat(vector(2), Vec(x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^100))) \\ _Colin Barker_, Aug 14 2017

%o (Python)

%o def A187322(n): return (n>>1)+(3*n>>2) # _Chai Wah Wu_, Jan 31 2023

%Y Cf. A008587, A016873, A016885, A004526, A057353.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Mar 08 2011