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A047477 Numbers that are congruent to {0, 5, 7} mod 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)