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A047281 Numbers that are congruent to {0, 3, 6} mod 7. 1
0, 3, 6, 7, 10, 13, 14, 17, 20, 21, 24, 27, 28, 31, 34, 35, 38, 41, 42, 45, 48, 49, 52, 55, 56, 59, 62, 63, 66, 69, 70, 73, 76, 77, 80, 83, 84, 87, 90, 91, 94, 97, 98, 101, 104, 105, 108, 111, 112, 115, 118, 119, 122, 125, 126, 129, 132, 133, 136, 139, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

a(n+1) = 3*n - 2*floor(n/3). - Gary Detlefs, Mar 27 2010

G.f.: x^2*(3+3*x+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (21*n-15+6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-4, a(3k-2) = 7k-7. (End)

a(n) = Sum_{i=1..n-1} numerator(3/i). - Wesley Ivan Hurt, Feb 26 2017

MAPLE

seq(3*n - 2*floor(n/3), n=0..52); # Gary Detlefs, Mar 27 2010

MATHEMATICA

Select[Range[0, 150], MemberQ[{0, 3, 6}, Mod[#, 7]]&] (* Harvey P. Dale, Oct 05 2012 *)

LinearRecurrence[{1, 0, 1, -1}, {0, 3, 6, 7}, 70] (* Vincenzo Librandi, Feb 28 2017 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 3, 6]]; // Wesley Ivan Hurt, Jun 07 2016

(PARI) a(n)=3*n - 3 - (n-1)\3*2 \\ Charles R Greathouse IV, Feb 28 2017

CROSSREFS

Sequence in context: A045412 A288215 A284625 * A182909 A269903 A191103

Adjacent sequences:  A047278 A047279 A047280 * A047282 A047283 A047284

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)