A047478 Numbers that are congruent to {1, 5, 7} mod 8.

1, 5, 7, 9, 13, 15, 17, 21, 23, 25, 29, 31, 33, 37, 39, 41, 45, 47, 49, 53, 55, 57, 61, 63, 65, 69, 71, 73, 77, 79, 81, 85, 87, 89, 93, 95, 97, 101, 103, 105, 109, 111, 113, 117, 119, 121, 125, 127, 129, 133, 135, 137, 141, 143, 145, 149, 151, 153, 157, 159

Offset

1,2

Links

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

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

Formula

G.f.: x*(1+4*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 16 2012

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

a(n) = (24*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-7. (End)

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

Maple

A047478:=n->(24*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047478(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 300], MemberQ[{1, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

Prog

(Magma) I:=[1, 5, 7, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 16 2012

Crossrefs

Cf. A047484, A047529, A047623.

Sequence in context: A251627 A128161 A141106 * A048974 A089193 A302482

Adjacent sequences: A047475 A047476 A047477 * A047479 A047480 A047481

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved