A047484 Numbers that are congruent to {3, 5, 7} mod 8.

3, 5, 7, 11, 13, 15, 19, 21, 23, 27, 29, 31, 35, 37, 39, 43, 45, 47, 51, 53, 55, 59, 61, 63, 67, 69, 71, 75, 77, 79, 83, 85, 87, 91, 93, 95, 99, 101, 103, 107, 109, 111, 115, 117, 119, 123, 125, 127, 131, 133, 135, 139, 141, 143, 147, 149, 151, 155, 157, 159

Offset

1,1

Links

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

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

Formula

G.f.: x*(3+2*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 14 2012]

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, May 17 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = (24*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-5. (End)

a(n) = 3*n - floor((n-1)/3) - ((n-1) mod 3). - Wesley Ivan Hurt, Sep 26 2017

a(n) = 2*(n + floor((n-1)/3)) + 1. - Wolfdieter Lang, Sep 11 2021

Maple

A047484:=n->(24*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047484(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 300], MemberQ[{3, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 17 2012 *)

Prog

(Magma) I:=[3, 5, 7, 11]; [n le 4 select I[n] else Self(n-1)+Self(n-3) -Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 17 2012

Crossrefs

Cf. A047478, A047529, A047623.

Sequence in context: A283680 A005239 A141107 * A036991 A165887 A316625

Adjacent sequences: A047481 A047482 A047483 * A047485 A047486 A047487

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved