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A047258 Numbers that are congruent to {0, 4, 5} mod 6. 3
0, 4, 5, 6, 10, 11, 12, 16, 17, 18, 22, 23, 24, 28, 29, 30, 34, 35, 36, 40, 41, 42, 46, 47, 48, 52, 53, 54, 58, 59, 60, 64, 65, 66, 70, 71, 72, 76, 77, 78, 82, 83, 84, 88, 89, 90, 94, 95, 96, 100, 101, 102, 106, 107, 108, 112, 113, 114, 118, 119, 120, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

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

FORMULA

G.f.: x^2*(4+x+x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Apr 13 2015: (Start)

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

a(n) = 2n-2 + ((2n-2) mod 3). (End)

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = 2*n-1-2*sin(2*n*Pi/3)/sqrt(3).

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

E.g.f.: 1 + (2*x - 1)*exp(x) - 2*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2))/sqrt(3). - Ilya Gutkovskiy, Jun 14 2016

MAPLE

A047258:=n->2*n-2+((2*n-2) mod 3): seq(A047258(n), n=1..100); # Wesley Ivan Hurt, Apr 13 2015

MATHEMATICA

Flatten[#+{0, 4, 5}&/@(6Range[0, 20])] (* Harvey P. Dale, Jul 20 2011 *)

Select[Range[0, 200], MemberQ[{0, 4, 5}, Mod[#, 6]] &] (* Vincenzo Librandi, Apr 14 2015 *)

PROG

(MAGMA) [2*n-2+((2*n-2) mod 3) : n in [1..100]]; // Wesley Ivan Hurt, Apr 13 2015

(PARI) concat (0, Vec(x^2*(4+x+x^2)/((1+x+x^2)*(x-1)^2) + O(x^80))) \\ Michel Marcus, Apr 14 2015

CROSSREFS

Cf. A047245 (complement).

Sequence in context: A246441 A026312 A070751 * A024565 A327223 A143833

Adjacent sequences:  A047255 A047256 A047257 * A047259 A047260 A047261

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, Apr 13 2015

STATUS

approved

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Last modified October 16 23:30 EDT 2019. Contains 328103 sequences. (Running on oeis4.)