A187326 a(n) = floor(n/4) + floor(n/2) + floor(3n/4).

0, 0, 2, 3, 6, 6, 8, 9, 12, 12, 14, 15, 18, 18, 20, 21, 24, 24, 26, 27, 30, 30, 32, 33, 36, 36, 38, 39, 42, 42, 44, 45, 48, 48, 50, 51, 54, 54, 56, 57, 60, 60, 62, 63, 66, 66, 68, 69, 72, 72, 74, 75, 78, 78, 80, 81, 84, 84, 86, 87, 90, 90, 92, 93, 96, 96, 98, 99, 102, 102, 104, 105, 108, 108, 110, 111, 114, 114, 116, 117

Offset: 0

Author

Clark Kimberling, Mar 08 2011

Keywords

• nonn
• easy

Examples

			G.f. = 2*x^2 + 3*x^3 + 6*x^4 + 6*x^5 + 8*x^6 + 9*x^7 + 12*x^8 + 12*x^9 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A187333.

Programs

Magma

[Floor(n/4)+Floor(n/2)+Floor(3*n/4): n in [0..90] ]; // Vincenzo Librandi, Jul 18 2011

Mathematica

Table[Floor[n/4]+Floor[n/2]+Floor[3n/4], {n,0,120}]
LinearRecurrence[{1,0,0,1,-1},{0,0,2,3,6},100] (* Harvey P. Dale, May 27 2016 *)

PARI

{a(n) = (3*n - n%2) / 2 - (n%4!=0)}; /* Michael Somos, Feb 23 2014 */

PARI

a(n)=n\4 + n\2 + 3*n\4 \\ Charles R Greathouse IV, Jul 19 2016

Formula

G.f.: x^2*(2+x+3*x^2) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Mar 08 2011

a(n) = +1*a(n-1) +1*a(n-4) -1*a(n-5). - Joerg Arndt, Apr 01 2011

a(n) = (6*(n-1)+(1+(-1)^n)*(2+i^n))/4, where i=sqrt(-1). - Bruno Berselli, Mar 08 2011

a(n) = (3*n-4+gcd(4,n))/2. - Jose Eduardo Blazek, Mar 22 2014

a(n+1) = a(n)+(3+gcd(4,n+1)-gcd(4,n))/2 and a(0)=0. - Jose Eduardo Blazek, Mar 23 2014

a(n+4) = a(n) + 6. - Michael Somos, Feb 23 2014