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A047244 Numbers that are congruent to {0, 2, 3} mod 6. 3
0, 2, 3, 6, 8, 9, 12, 14, 15, 18, 20, 21, 24, 26, 27, 30, 32, 33, 36, 38, 39, 42, 44, 45, 48, 50, 51, 54, 56, 57, 60, 62, 63, 66, 68, 69, 72, 74, 75, 78, 80, 81, 84, 86, 87, 90, 92, 93, 96, 98, 99, 102, 104, 105, 108, 110, 111, 114, 116, 117, 120, 122, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..63.

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

FORMULA

G.f.: x^2*(2+x+3*x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

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

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

a(n) = (6*n-7-2*cos(2*n*Pi/3))/3.

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

E.g.f.: (9 + (6*x - 7)*exp(x) - 2*cos(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2)))/3. - Ilya Gutkovskiy, Jun 14 2016

MAPLE

A047244:=n->(6*n-7-2*cos(2*n*Pi/3))/3: seq(A047244(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

MATHEMATICA

Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 2 || Mod[#, 6] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)

Select[Range[0, 200], MemberQ[{0, 2, 3}, Mod[#, 6]] &] (* Vincenzo Librandi, Oct 02 2015 *)

LinearRecurrence[{1, 0, 1, -1}, {2, 3, 6, 8}, {0, 20}] (* Eric W. Weisstein, Apr 09 2018 *)

CoefficientList[Series[x (2 + x + 3 x^2)/((-1 + x)^2 (1 + x + x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 09 2018 *)

Table[(6 n + Cos[2 n Pi/3] + Sqrt[3] Sin[2 n Pi/3] - 1)/3, {n, 0, 20}] (* Eric W. Weisstein, Apr 09 2018 *)

PROG

(PARI) isok(n) = my(m = n % 6); (m==0) || (m==2) || (m==3); \\ Michel Marcus, Oct 02 2015

(MAGMA) [n : n in [0..130] | n mod 6 in [0, 2, 3]]; // Vincenzo Librandi, Oct 02 2015

CROSSREFS

Cf. A047240, A047242.

Sequence in context: A032711 A135768 A287659 * A111215 A099381 A289943

Adjacent sequences:  A047241 A047242 A047243 * A047245 A047246 A047247

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)