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A047491
Numbers that are congruent to {4, 5, 7} mod 8.
1
4, 5, 7, 12, 13, 15, 20, 21, 23, 28, 29, 31, 36, 37, 39, 44, 45, 47, 52, 53, 55, 60, 61, 63, 68, 69, 71, 76, 77, 79, 84, 85, 87, 92, 93, 95, 100, 101, 103, 108, 109, 111, 116, 117, 119, 124, 125, 127, 132, 133, 135, 140, 141, 143, 148, 149, 151, 156, 157
OFFSET
1,1
FORMULA
G.f.: x*(4+x+2*x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Nov 06 2015
From Wesley Ivan Hurt, Jun 09 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-4. (End)
MAPLE
A047491:=n->(24*n-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047491(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {4, 5, 7, 12}, 60] (* Harvey P. Dale, Feb 06 2019 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [4, 5, 7]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
Sequence in context: A129302 A216536 A051658 * A064401 A079337 A160934
KEYWORD
nonn,easy
STATUS
approved