A047342 - OEIS

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..61.

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

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)

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 *)

PROG

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

CROSSREFS

Cf. A168223, A168224.

Sequence in context: A295399 A257507 A003669 * A334469 A228854 A257508

Adjacent sequences: A047339 A047340 A047341 * A047343 A047344 A047345

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved