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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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)

Programs

Magma

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

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 *)

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

Extensions

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