A047618 Numbers that are congruent to {0, 2, 5} mod 8.

0, 2, 5, 8, 10, 13, 16, 18, 21, 24, 26, 29, 32, 34, 37, 40, 42, 45, 48, 50, 53, 56, 58, 61, 64, 66, 69, 72, 74, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 104, 106, 109, 112, 114, 117, 120, 122, 125, 128, 130, 133, 136, 138, 141, 144, 146, 149, 152, 154, 157, 160, 162

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(n) = 3*(n - 1) - floor((n - 1)/3) - ((n - 1)^2 % 3). - Gary Detlefs, Mar 19 2010; corrected by L. Edson Jeffery, Sep 02 2014

a(n) = floor(8*(n-1)/3). - Gary Detlefs, Jan 02 2012

G.f.: x^2*(2+3*x+3*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Feb 03 2014

Conjecture: a(n)+a(n+1)+a(n+2) = 8*n-1; or a(n) = 8*(n-2)-a(n-1)-a(n-2)-1, n>3, with a(1)=0, a(2)=2, a(3)=5. - L. Edson Jeffery, Sep 02 2014

a(n) = a(n-1)+a(n-3)-a(n-4), n>4, with a(1)=0, a(2)=2, a(3)=5, a(4)=8. - L. Edson Jeffery, Sep 02 2014

a(n) = ((8*n-9)+2*sin((2*n*Pi)/3)/sqrt(3))/3. - L. Edson Jeffery, Sep 02 2014

a(3k) = 8k-3, a(3k-1) = 8k-6, a(3k-2) = 8k-8. - Wesley Ivan Hurt, Jun 10 2016

Maple

seq(3*n - floor(n/3) - (n^2 mod 3), n=0..51); # Gary Detlefs, Mar 19 2010

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {0, 2, 5, 8}, 62] (* L. Edson Jeffery, Sep 02 2014 *)
Table[((8*n-9)+2*Sin[(2*n*Pi)/3]/Sqrt[3])/3, {n, 62}] (* L. Edson Jeffery, Sep 02 2014 *)
Table[8 n + {0, 2, 5}, {n, 0, 100}]//Flatten (* Vincenzo Librandi, Jun 11 2016 *)

Prog

(PARI) a(n) = floor(8*(n-1)/3); \\ Michel Marcus, Sep 03 2014
(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 5]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A039770 A236019 A247426 * A236535 A059551 A330094

Adjacent sequences: A047615 A047616 A047617 * A047619 A047620 A047621

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved