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A047234 Numbers that are congruent to {0, 1, 4} mod 6. 8
0, 1, 4, 6, 7, 10, 12, 13, 16, 18, 19, 22, 24, 25, 28, 30, 31, 34, 36, 37, 40, 42, 43, 46, 48, 49, 52, 54, 55, 58, 60, 61, 64, 66, 67, 70, 72, 73, 76, 78, 79, 82, 84, 85, 88, 90, 91, 94, 96, 97, 100, 102, 103, 106, 108, 109, 112, 114, 115, 118, 120, 121, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

Equals partial sums of (0, 1, 3, 2, 1, 3, 2, 1, 3, 2, ...). - Gary W. Adamson, Jun 19 2008

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

From Wesley Ivan Hurt, Jun 14 2016: (Start)

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

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

a(3k) = 6k-2, a(3k-1) = 6k-5, a(3k-2) = 6k-6. (End)

MAPLE

A047234:=n->(6*n-7+cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047234(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

MATHEMATICA

Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 4 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)

LinearRecurrence[{1, 0, 1, -1}, {0, 1, 4, 6}, 100] (* Vincenzo Librandi, Jun 15 2016 *)

PROG

(PARI) a(n)=(n-1)\3*6+[4, 0, 1][n%3+1] \\ Charles R Greathouse IV, Jun 11 2015

(MAGMA) [n : n in [0..150] | n mod 6 in [0, 1, 4]]; // Wesley Ivan Hurt, Jun 14 2016

CROSSREFS

Cf. A047240, A047242.

Sequence in context: A272632 A229744 A191920 * A089532 A103401 A107622

Adjacent sequences:  A047231 A047232 A047233 * A047235 A047236 A047237

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 23 22:33 EDT 2016. Contains 275767 sequences.