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A047618 Numbers that are congruent to {0, 2, 5} mod 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A189535

Adjacent sequences:  A047615 A047616 A047617 * A047619 A047620 A047621

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 20 17:44 EST 2018. Contains 297961 sequences.