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A047459
Numbers that are congruent to {1, 3, 4} mod 8.
2
1, 3, 4, 9, 11, 12, 17, 19, 20, 25, 27, 28, 33, 35, 36, 41, 43, 44, 49, 51, 52, 57, 59, 60, 65, 67, 68, 73, 75, 76, 81, 83, 84, 89, 91, 92, 97, 99, 100, 105, 107, 108, 113, 115, 116, 121, 123, 124, 129, 131, 132, 137, 139, 140, 145, 147, 148, 153, 155, 156
OFFSET
1,2
COMMENTS
Numbers m such that Lucas(m) mod 3 = 1. - Bruno Berselli, Oct 19 2017
FORMULA
G.f.: x*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x+x^2)). - Colin Barker, May 13 2012
From Wesley Ivan Hurt, Jun 09 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*(12*n-12-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 8*k-4, a(3*k-1) = 8*k-5, a(3*k-2) = 8*k-7. (End)
MAPLE
A047459:=n->2*(12*n-12-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047459(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
Select[Range[200], MemberQ[{1, 3, 4}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 3, 4, 9}, 60] (* Harvey P. Dale, Nov 26 2015 *)
PROG
(Magma) [n: n in [0..150] | n mod 8 in [1, 3, 4]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
Cf. A000032.
Cf. A016825: numbers m such that Lucas(m) mod 3 = 0.
Cf. A047477: numbers m such that Lucas(m) mod 3 = 2.
Sequence in context: A336930 A035252 A227939 * A177943 A091380 A321871
KEYWORD
nonn,easy
STATUS
approved