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A047303 Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 7. 1
0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Complement of A017041. - Michel Marcus, Sep 08 2015

LINKS

Table of n, a(n) for n=1..66.

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

FORMULA

G.f.: x^2*(1+x+x^2+x^3+2*x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Sep 07 2015: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = n + 1 + floor((n-2)/6) - ceiling((n-1)/6) + floor((n-1)/6) - ceiling(n/6) + floor(n/6). (End)

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = (42*n - 51 + 3*cos(n*Pi) + 4*sqrt(3)*cos((1-4*n)*Pi/6) + 12*sin((1+2*n)*Pi/6))/36.

a(6k) = 7k-1, a(6k-1) = 7k-3, a(6k-2) = 7k-4, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)

MAPLE

A047303:=n->n+1+floor((n-2)/6)-ceil((n-1)/6)+floor((n-1)/6)-ceil(n/6)+floor(n/6): seq(A047303(n), n=1..100); # Wesley Ivan Hurt, Sep 07 2015

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4, 6}, Mod[#, 7]] &] (* Vincenzo Librandi, Sep 08 2015 *)

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 6, 7}, 80] (* Harvey P. Dale, Sep 24 2016 *)

PROG

(MAGMA) [n: n in [0..100] | n mod 7 in [0..4] cat [6]]; // Vincenzo Librandi, Sep 08 2015

CROSSREFS

Cf. A017041 (7n+5).

Sequence in context: A141451 A285211 A183217 * A057906 A039214 A032866

Adjacent sequences:  A047300 A047301 A047302 * A047304 A047305 A047306

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Sep 08 2015

STATUS

approved

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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)