A047364 Numbers that are congruent to {3, 4, 5} mod 7.

3, 4, 5, 10, 11, 12, 17, 18, 19, 24, 25, 26, 31, 32, 33, 38, 39, 40, 45, 46, 47, 52, 53, 54, 59, 60, 61, 66, 67, 68, 73, 74, 75, 80, 81, 82, 87, 88, 89, 94, 95, 96, 101, 102, 103, 108, 109, 110, 115, 116, 117, 122, 123, 124, 129, 130, 131, 136, 137, 138, 143

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

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

Formula

G.f.: x*(3+x+x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 08 2016: (Start)

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

a(n) = (21*n-6-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047364:=n->(21*n-6-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047364(n), n=1..100); # Wesley Ivan Hurt, Jun 08 2016

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {3, 4, 5, 10}, 60] (* Harvey P. Dale, Dec 03 2014 *)
Flatten[# + {3, 4, 5} & /@ (7 Range[0, 20])] (* or *)
Select[Range[0, 150], MemberQ[{3, 4, 5}, Mod[#, 7]] &] (* Robert G. Wilson v, Sep 26 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [3..5]]; // Wesley Ivan Hurt, Jun 08 2016
(PARI) a(n)=(n-1)\3*7 + (n-1)%3 + 3 \\ Charles R Greathouse IV, Sep 26 2016

Crossrefs

Sequence in context: A014463 A340015 A161983 * A274519 A139445 A185345

Adjacent sequences: A047361 A047362 A047363 * A047365 A047366 A047367

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved