A187331 a(n) = Sum_{k=1..4} floor(k*n/4).

0, 1, 4, 6, 10, 11, 14, 16, 20, 21, 24, 26, 30, 31, 34, 36, 40, 41, 44, 46, 50, 51, 54, 56, 60, 61, 64, 66, 70, 71, 74, 76, 80, 81, 84, 86, 90, 91, 94, 96, 100, 101, 104, 106, 110, 111, 114, 116, 120, 121, 124, 126, 130, 131, 134, 136, 140, 141, 144, 146, 150, 151, 154, 156, 160, 161, 164

Offset: 0

Author

Clark Kimberling, Mar 08 2011

Keywords

• nonn

Links

• M. F. Hasler, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A187332 (complement), A187326 (= a(n) - n), A187333.

Programs

Mathematica

t=Table[Sum[Floor[k*n/4], {k,1,4}],{n,0,200}]  (* A187331 *)
Complement[Range[Length[t]], t]                (* A187332 *)

PARI

A187331(n)=n\4+n\2+3*n\4+n \\ M. F. Hasler, Nov 21 2017

Formula

From Chai Wah Wu, Jun 07 2016: (Start)

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

G.f.: x*(4*x^3 + 2*x^2 + 3*x + 1)/(x^5 - x^4 - x + 1). (End)

a(n) = n + A187326(n), where A187326(n) = [n/4] + [n/2] + [3n/4], [.] = floor. - M. F. Hasler, Nov 21 2017