A047623 Numbers that are congruent to {1, 3, 5} mod 8.

1, 3, 5, 9, 11, 13, 17, 19, 21, 25, 27, 29, 33, 35, 37, 41, 43, 45, 49, 51, 53, 57, 59, 61, 65, 67, 69, 73, 75, 77, 81, 83, 85, 89, 91, 93, 97, 99, 101, 105, 107, 109, 113, 115, 117, 121, 123, 125, 129, 131, 133, 137, 139, 141, 145, 147, 149, 153, 155, 157

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

Formula

a(n) = 2*floor((n-1)/3) + 2*n - 1. - Gary Detlefs, Mar 18 2010

From Colin Barker, Feb 03 2012: (Start)

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)

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

a(n) = (24*n-21-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-3, a(3k-1) = 8k-5, a(3k-2) = 8k-7. (End)

Maple

A047623:=n->(24*n-21-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047623(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 3, 5}, Mod[#, 8]]&] (* Vincenzo Librandi, Apr 27 2012 *)

Prog

(Magma) I:=[1, 3, 5, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 27 2012

Crossrefs

Cf. A047478, A047484, A047529.

Sequence in context: A294427 A141231 A287344 * A190523 A161781 A007950

Adjacent sequences: A047620 A047621 A047622 * A047624 A047625 A047626

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved