A047616 Numbers that are congruent to {0, 1, 5} mod 8.

0, 1, 5, 8, 9, 13, 16, 17, 21, 24, 25, 29, 32, 33, 37, 40, 41, 45, 48, 49, 53, 56, 57, 61, 64, 65, 69, 72, 73, 77, 80, 81, 85, 88, 89, 93, 96, 97, 101, 104, 105, 109, 112, 113, 117, 120, 121, 125, 128, 129, 133, 136, 137, 141, 144, 145, 149, 152, 153, 157

Offset

1,3

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

From Wesley Ivan Hurt, Jun 09 2016: (Start)

G.f.: x^2*(1+4*x+3*x^2)/((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-30+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-3, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

Maple

A047616:=n->(24*n-30+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047616(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
Table[8 n + {0, 1, 5}, {n, 0, 200}]//Flatten (* Vincenzo Librandi, Jun 11 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 5, 8}, 60] (* Harvey P. Dale, Jul 20 2024 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 5]]; // Wesley Ivan Hurt, Jun 09 2016
(PARI) a(n)=n\3*8+[-3, 0, 1][n%3+1] \\ Charles R Greathouse IV, Jul 19 2016

Crossrefs

Sequence in context: A213881 A179832 A334919 * A287551 A375713 A231065

Adjacent sequences: A047613 A047614 A047615 * A047617 A047618 A047619

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved