A047317 Numbers that are congruent to {1, 2, 4, 5, 6} mod 7.

1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 34, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 50, 51, 53, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 76, 78, 79

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = a(n-1) + a(n-5) - a(n-6).

a(n) = floor((7*n-1)/5). - Gary Detlefs, May 14 2001

G.f.: x*(1 + x + 2*x^2 + x^3 + x^4 + x^5) / ( (x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011

Mathematica

CoefficientList[Series[(1 + x + 2 x^2 + x^3 + x^4 + x^5) / ((x^4 + x^3 + x^2 + x + 1) (x - 1)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 26 2013 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 4, 5, 6, 8}, 100] (* Harvey P. Dale, Apr 02 2017 *)

Prog

(Magma) [n: n in [1..80] | n mod 7 in [1, 2, 4, 5, 6]]; // Vincenzo Librandi, Jul 26 2013

Crossrefs

Sequence in context: A039032 A000062 A247964 * A376953 A288998 A289026

Adjacent sequences: A047314 A047315 A047316 * A047318 A047319 A047320

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved