A047381 Numbers that are congruent to {0, 1, 2, 4, 5} mod 7.

0, 1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 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

a(n) = floor( (7/5)(n-1) ). [Gary Detlefs, Feb 20 2010]

From R. J. Mathar, Mar 11 2011: (Start)

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

G.f.: x^2*(1 + x + 2*x^2 + x^3 + 2*x^4) / ((x^4 + x^3 + x^2 + x + 1)*(x-1)^2). (End)

5*a(n) = 7*n-9-b(n) where b(n) = b(n-5) = 1, -2, 0, 2, -1 (for offset 0). - R. J. Mathar, Jul 22 2020

Maple

seq(floor((7/5)*(n-1)), n=1..56); # Gary Detlefs, Feb 20 2010

Mathematica

CoefficientList[Series[x (1 + x + 2 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 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 7}, 80] (* Harvey P. Dale, Oct 04 2023 *)

Prog

(Magma) [ n: n in [1..80] | n mod 7 in [0, 1, 2, 4, 5] ]; // Vincenzo Librandi, Jul 26 2013

Crossrefs

Sequence in context: A346128 A276220 A288204 * A286428 A329996 A258833

Adjacent sequences: A047378 A047379 A047380 * A047382 A047383 A047384

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Formula and Maple code adapted to the offset by Wesley Ivan Hurt, Jul 16 2013

Status

approved