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A047623 Numbers that are congruent to {1, 3, 5} mod 8. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified May 17 07:36 EDT 2021. Contains 343966 sequences. (Running on oeis4.)