A047342 Numbers that are congruent to {0, 3, 4} mod 7.

0, 3, 4, 7, 10, 11, 14, 17, 18, 21, 24, 25, 28, 31, 32, 35, 38, 39, 42, 45, 46, 49, 52, 53, 56, 59, 60, 63, 66, 67, 70, 73, 74, 77, 80, 81, 84, 87, 88, 91, 94, 95, 98, 101, 102, 105, 108, 109, 112, 115, 116, 119, 122, 123, 126, 129, 130, 133, 136, 137, 140

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Record values in A168223: a(n) = A168223(A168224(n)) and A168223(m) < a(n) for m < A168224(n). - Reinhard Zumkeller, Nov 20 2009

Also: Numbers n such that kronecker(n^2-4,7) = -1. - M. F. Hasler, Mar 14 2013

Links

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

Crossrefs

Cf. A168223, A168224.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 3, 4]]; // Wesley Ivan Hurt, Jun 13 2016

Maple

A047342:=n->(21*n-21-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047342(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0,150], MemberQ[{0,3,4}, Mod[#,7]]&] (* Harvey P. Dale, Mar 18 2011 *)
CoefficientList[Series[(3x+x^2+3x^3)/((-1+x)^2(1+x+x^2)),{x,0,160}],x] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
LinearRecurrence[{1, 0, 1, -1},{0, 3, 4, 7},61] (* Ray Chandler, Aug 25 2015 *)

Formula

G.f.: x(3+x+3x^2)/((1-x)^2*(1+x+x^2)). - R. J. Mathar, Sep 17 2008

a(n) = a(n-1) + a(n-3) - a(n-4), n>4. - Vincenzo Librandi, Mar 24 2011

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

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

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