A110657 a(n) = A028242(A028242(n)).

0, 1, 2, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 11, 9, 10, 11, 12, 10, 11, 12, 13, 11, 12, 13, 14, 12, 13, 14, 15, 13, 14, 15, 16, 14, 15, 16, 17, 15, 16, 17, 18, 16, 17, 18, 19, 17, 18, 19, 20, 18, 19, 20, 21, 19, 20, 21

Offset

0,3

Comments

Also array read by rows, with four columns, in which row n lists n, n+1, n+2, n. - Omar E. Pol, Jan 22 2012

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).

Formula

A110658(n) = A028242(a(n)) = a(A028242(n)).

a(n) = floor(n/4) + (n mod 4) mod 3.

From Bruno Berselli, Sep 28 2011: (Start)

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

a(n) = (1/8)*(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3). (End)

From Wesley Ivan Hurt, Apr 12 2015: (Start)

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

a(n) = 1 + floor((n-7)/4) + ((n-7) mod 4). (End)

a(n) = n - 3*floor((n+1)/4). - Gionata Neri, Oct 19 2015

a(n) = (2*n+3-6*cos(n*Pi/2)+3*cos(n*Pi)+6*sin(n*Pi/2))/8. - Wesley Ivan Hurt, Oct 01 2017

Sum_{n>=4} (-1)^(n+1)/a(n) = 1/2. - Amiram Eldar, Oct 04 2022

Example

From Omar E. Pol, Jan 22 2012: (Start)
Array begins:
0, 1, 2, 0;
1, 2, 3, 1;
2, 3, 4, 2;
3, 4, 5, 3;
4, 5, 6, 4;
5, 6, 7, 5;
6, 7, 8, 6;
7, 8, 9, 7;
(End)

Maple

A110657:=n->(1/8)*(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3): seq(A110657(n), n=0..100); # Wesley Ivan Hurt, Apr 12 2015

Mathematica

Table[(1/8)*(2*n - 6*(-1)^(n*(n + 1)/2) + 3*(-1)^n + 3), {n, 0, 100}] (* Wesley Ivan Hurt, Apr 12 2015 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 0, 1}, 90] (* Harvey P. Dale, Feb 02 2020 *)

Prog

(Magma) [Integers()!(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3)/8: n in [0..81]]; // Bruno Berselli, Sep 28 2011
(PARI) vector(80, n, n--; 1 + (n-7)\4 + ((n-7) % 4)) \\ Michel Marcus, Apr 13 2015

Crossrefs

Cf. A007892, A110655.

Sequence in context: A336684 A046695 A071433 * A071512 A263136 A080018

Adjacent sequences: A110654 A110655 A110656 * A110658 A110659 A110660

Keyword

nonn,tabf,easy

Author

Reinhard Zumkeller, Aug 05 2005

Status

approved