A047205 Numbers that are congruent to {0, 3, 4} mod 5.

0, 3, 4, 5, 8, 9, 10, 13, 14, 15, 18, 19, 20, 23, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 40, 43, 44, 45, 48, 49, 50, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 73, 74, 75, 78, 79, 80, 83, 84, 85, 88, 89, 90, 93, 94, 95, 98, 99, 100, 103, 104, 105, 108

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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

Formula

G.f.: x^2*(3+x+x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

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

a(n) = (15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/5 - sqrt(1-2/sqrt(5))*Pi/5. - Amiram Eldar, Jan 01 2022

Maple

A047205:=n->(15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047205(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

Prog

(Magma) [ n : n in [0..150] | n mod 5 in [0, 3, 4] ]; // Vincenzo Librandi, Mar 31 2011
(PARI) a(n)=n\3*5+[-1, 0, 3][n%3+1] \\ Charles R Greathouse IV, Dec 22 2011

Crossrefs

Sequence in context: A173999 A127427 A286994 * A283765 A120631 A047601

Adjacent sequences: A047202 A047203 A047204 * A047206 A047207 A047208

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved