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A047391 Numbers that are congruent to {1, 3, 5} mod 7. 3
1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 33, 36, 38, 40, 43, 45, 47, 50, 52, 54, 57, 59, 61, 64, 66, 68, 71, 73, 75, 78, 80, 82, 85, 87, 89, 92, 94, 96, 99, 101, 103, 106, 108, 110, 113, 115, 117, 120, 122, 124, 127, 129, 131, 134, 136, 138, 141 (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

From Bruno Berselli, Mar 25 2011:  (Start)

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

a(n) = 7*floor((n-1)/3)+2*(n-1 mod 3)+1.

a(n) = (1/3)*(7*n-5-A049347(n)). (End)

From Wesley Ivan Hurt, Jun 13 2016: (Start)

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

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

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

MAPLE

A047391:=n->(21*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9: seq(A047391(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{1, 3, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)

LinearRecurrence[{1, 0, 1, -1}, {1, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(MAGMA) [n: n in [1..122] | n mod 7 in [1, 3, 5]]; // Bruno Berselli, Mar 25 2011

CROSSREFS

Cf. A049347.

Sequence in context: A184584 A191160 A189929 * A184655 A090846 A195170

Adjacent sequences:  A047388 A047389 A047390 * A047392 A047393 A047394

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 27 11:11 EDT 2016. Contains 275905 sequences.