A047396 Numbers that are congruent to {1, 2, 6} mod 8.

1, 2, 6, 9, 10, 14, 17, 18, 22, 25, 26, 30, 33, 34, 38, 41, 42, 46, 49, 50, 54, 57, 58, 62, 65, 66, 70, 73, 74, 78, 81, 82, 86, 89, 90, 94, 97, 98, 102, 105, 106, 110, 113, 114, 118, 121, 122, 126, 129, 130, 134, 137, 138, 142, 145, 146, 150, 153, 154, 158

Offset

1,2

Comments

Numbers n such that the determinant of the character table of the cyclic group C_n is an integer (for every n this determinant has degree at most 2 over the rationals Q). - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001

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+4*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 05 2011

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=2, a(3)=6, a(4)=9. - Harvey P. Dale, Sep 30 2012

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

a(n) = (24*n-21+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)

Maple

A047396:=n->(24*n-21+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047396(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Flatten[#+{1, 2, 6}&/@(8*Range[0, 20])] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 2, 6, 9}, 80] (* Harvey P. Dale, Sep 30 2012 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 6]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A016726 A360136 A359821 * A276936 A276937 A243373

Adjacent sequences: A047393 A047394 A047395 * A047397 A047398 A047399

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved