A047465 Numbers that are congruent to {1, 2, 4} mod 8.

1, 2, 4, 9, 10, 12, 17, 18, 20, 25, 26, 28, 33, 34, 36, 41, 42, 44, 49, 50, 52, 57, 58, 60, 65, 66, 68, 73, 74, 76, 81, 82, 84, 89, 90, 92, 97, 98, 100, 105, 106, 108, 113, 114, 116, 121, 122, 124, 129, 130, 132, 137, 138, 140, 145, 146, 148, 153, 154, 156

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(1+x+2*x^2+4*x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 14 2012]

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, May 16 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = 8*n/3-3-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3k) = 8k-4, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)

Maple

A047465:=n->8*n/3-3-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047465(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 300], MemberQ[{1, 2, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

Prog

(Magma) I:=[1, 2, 4, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 16 2012

Crossrefs

Sequence in context: A072583 A178488 A226821 * A365343 A002258 A252760

Adjacent sequences: A047462 A047463 A047464 * A047466 A047467 A047468

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved