A047619 Numbers that are congruent to {1, 2, 5} mod 8.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

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: A055394 A078360 A114995 * A046711 A191171 A191776

Adjacent sequences: A047616 A047617 A047618 * A047620 A047621 A047622

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved