A047477 Numbers that are congruent to {0, 5, 7} mod 8.

0, 5, 7, 8, 13, 15, 16, 21, 23, 24, 29, 31, 32, 37, 39, 40, 45, 47, 48, 53, 55, 56, 61, 63, 64, 69, 71, 72, 77, 79, 80, 85, 87, 88, 93, 95, 96, 101, 103, 104, 109, 111, 112, 117, 119, 120, 125, 127, 128, 133, 135, 136, 141, 143, 144, 149, 151, 152, 157, 159

Offset

1,2

Comments

Numbers m such that Lucas(m) mod 3 = 2. - Bruno Berselli, Oct 19 2017

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^2*(5+2*x+x^2)/((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 - 12 + 3*cos(2*n*Pi/3) - 7*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047477:=n->(24*n-12+3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047477(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

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

Prog

(Magma) I:=[0, 5, 7, 8]; [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. A000032.

Cf. A016825: numbers m such that Lucas(m) mod 3 = 0.

Cf. A047459: numbers m such that Lucas(m) mod 3 = 1.

Sequence in context: A314374 A066001 A320391 * A216555 A288151 A242408

Adjacent sequences: A047474 A047475 A047476 * A047478 A047479 A047480

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved