A047591 Numbers that are congruent to {1, 6, 7} mod 8.

1, 6, 7, 9, 14, 15, 17, 22, 23, 25, 30, 31, 33, 38, 39, 41, 46, 47, 49, 54, 55, 57, 62, 63, 65, 70, 71, 73, 78, 79, 81, 86, 87, 89, 94, 95, 97, 102, 103, 105, 110, 111, 113, 118, 119, 121, 126, 127, 129, 134, 135, 137, 142, 143, 145, 150, 151, 153, 158, 159

Offset

1,2

Links

Table of n, a(n) for n=1..60.

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*(1+5*x+x^2+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-6-3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047591:=n->(24*n-6-3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047591(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
#+{1, 6, 7}&/@(8*Range[0, 20])//Flatten (* Harvey P. Dale, Jul 30 2022 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 6, 7]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A049304 A168614 A045014 * A340765 A239869 A289547

Adjacent sequences: A047588 A047589 A047590 * A047592 A047593 A047594

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved