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A047407 Numbers that are congruent to {0, 4, 6} mod 8. 1
0, 4, 6, 8, 12, 14, 16, 20, 22, 24, 28, 30, 32, 36, 38, 40, 44, 46, 48, 52, 54, 56, 60, 62, 64, 68, 70, 72, 76, 78, 80, 84, 86, 88, 92, 94, 96, 100, 102, 104, 108, 110, 112, 116, 118, 120, 124, 126, 128, 132, 134, 136, 140, 142, 144, 148, 150, 152, 156 (list; graph; refs; listen; history; text; internal format)
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

From R. J. Mathar, Dec 05 2011: (Start)

a(n) = 2*A004772(n).

G.f.: 2*x^2*(2+x+x^2) / ((1+x+x^2)*(x-1)^2). (End)

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9.

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

MAPLE

A047407:=n->2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047407(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

MATHEMATICA

Select[Range[0, 200], MemberQ[{0, 4, 6}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 4, 6, 8}, 70] (* Harvey P. Dale, Apr 20 2016 *)

PROG

(MAGMA) [n : n in [0..160] | n mod 8 in [0, 4, 6]]; // Vincenzo Librandi, May 02 2016

(PARI) a(n)=n\3*8+[-2, 0, 4][n%3+1] \\ Charles R Greathouse IV, May 02 2016

CROSSREFS

Cf. A004772.

Sequence in context: A241124 A117247 A249722 * A090697 A225508 A235036

Adjacent sequences:  A047404 A047405 A047406 * A047408 A047409 A047410

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)