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

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, 22, 23, 23, 25, 25, 26, 27, 28, 28, 30, 30, 31, 32, 33, 33, 35, 35, 36, 37, 38, 38, 40, 40, 41, 42, 43, 43, 45, 45, 46, 47, 48, 48, 50, 50, 51, 52, 53, 53, 55, 55, 56, 57, 58, 58, 60, 60

Offset: 1

Author

Simon Plouffe

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1).

Crossrefs

Cf. A001622, A010762, A110532.

Cf. A002264, A004526.

Programs

Magma

[Floor (n/2)+Floor(n/3): n in [0..100]]; // Vincenzo Librandi, Feb 22 2014

Maple

seq(floor(n/2) + floor(n/3), n=1..64);

Mathematica

Table[Floor[n/2] + Floor[n/3], {n, 100}] (* Wesley Ivan Hurt, Feb 21 2014 *)
LinearRecurrence[{0,1,1,0,-1},{0,1,2,3,3},80] (* Harvey P. Dale, May 05 2018 *)

PARI

a(n)=n\2+n\3

Formula

a(n) = A004526(n) + A002264(n). - Reinhard Zumkeller, Jul 25 2005

From Michael Somos, Aug 07 2005: (Start)

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

a(-n) = -2-a(n-1). (End)

a(n) = a(n-2)+a(n-3)-a(n-5). - Wesley Ivan Hurt, Jan 27 2022

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