A047367 Numbers that are congruent to {0, 1, 3, 4, 5} mod 7.

0, 1, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 67, 68, 70, 71, 73, 74, 75, 77, 78

Offset

1,3

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

G.f.: x^2*(1 + 2*x + x^2 + x^3 + 2*x^4) / ( (x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

Mathematica

CoefficientList[Series[x (1 + 2 x + x^2 + x^3 + 2 x^4) / ((x^4 + x^3 + x^2 + x + 1) (x - 1)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 26 2013 *)
#+{0, 1, 3, 4, 5}&/@(7*Range[0, 20])//Flatten (* or *) LinearRecurrence[ {1, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 7}, 80] (* Harvey P. Dale, Jun 05 2019 *)

Prog

(Magma) [n: n in [1..80] | n mod 7 in [0, 1, 3, 4, 5]]; // Vincenzo Librandi, Jul 26 2013

Crossrefs

Sequence in context: A330993 A184744 A063732 * A184620 A039043 A116591

Adjacent sequences: A047364 A047365 A047366 * A047368 A047369 A047370

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved