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A047619
Numbers that are congruent to {1, 2, 5} mod 8.
2
1, 2, 5, 9, 10, 13, 17, 18, 21, 25, 26, 29, 33, 34, 37, 41, 42, 45, 49, 50, 53, 57, 58, 61, 65, 66, 69, 73, 74, 77, 81, 82, 85, 89, 90, 93, 97, 98, 101, 105, 106, 109, 113, 114, 117, 121, 122, 125, 129, 130, 133, 137, 138, 141, 145, 146, 149, 153, 154, 157
OFFSET
1,2
FORMULA
From Wesley Ivan Hurt, Jun 09 2016: (Start)
G.f.: x*(1+x+3*x^2+3*x^3)/((x-1)^2*(1+x+x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-24-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-3, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)
MAPLE
A047619:=n->(24*n-24-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047619(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{1, 2, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
Table[8 n + {1, 2, 5}, {n, 0, 100}]//Flatten (* Vincenzo Librandi, Jun 11 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 5, 9}, 70] (* Harvey P. Dale, Aug 30 2021 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 5]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
Sequence in context: A078360 A372886 A114995 * A046711 A376848 A191171
KEYWORD
nonn,easy
STATUS
approved