A187322 a(n) = floor(n/2) + floor(3*n/4).

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

Offset: 0

Author

Clark Kimberling, Mar 08 2011

Keywords

• nonn
• easy

Comments

List of quadruples [5*k, 5*k, 5*k+2, 5*k+3]. - Luce ETIENNE, Aug 14 2017

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

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

Programs

Mathematica

Table[Floor[n/2]+Floor[3n/4], {n,0,120}]
LinearRecurrence[{1,0,0,1,-1},{0,0,2,3,5},80] (* Harvey P. Dale, Dec 05 2018 *)

PARI

a(n) = n\2 + 3*n\4; \\ Altug Alkan, Aug 14 2017

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

Python

def A187322(n): return (n>>1)+(3*n>>2) # Chai Wah Wu, Jan 31 2023

Formula

a(n) = A004526(n) + A057353(n). - Michel Marcus, Aug 14 2017

a(n) = (10*n-5+3*cos(n*Pi)+2*(cos(n*Pi/2)-sin(n*Pi/2)))/8. - Luce ETIENNE, Aug 14 2017

From Colin Barker, Aug 14 2017: (Start)

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

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

(End)