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A047259 Numbers that are congruent to {1, 4, 5} mod 6. 4
1, 4, 5, 7, 10, 11, 13, 16, 17, 19, 22, 23, 25, 28, 29, 31, 34, 35, 37, 40, 41, 43, 46, 47, 49, 52, 53, 55, 58, 59, 61, 64, 65, 67, 70, 71, 73, 76, 77, 79, 82, 83, 85, 88, 89, 91, 94, 95, 97, 100, 101, 103, 106, 107, 109, 112, 113, 115, 118, 119, 121, 124 (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, Feb 21 2009: (Start)

G.f.: x*(1+3*x+x^2+x^3)/((1-x)^2*(1+x+x^2)); a(n) = a(n-3) + 6. (End)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=4, a(3)=5, a(4)=7. - Harvey P. Dale, Feb 16 2015

From Wesley Ivan Hurt, Jun 11 2016: (Start)

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

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

MAPLE

A047259:=n->(6*n-2-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3: seq(A047259(n), n=1..100); # Wesley Ivan Hurt, Jun 11 2016

MATHEMATICA

Select[Range[200], MemberQ[{1, 4, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 4, 5, 7}, 100] (* Harvey P. Dale, Feb 16 2015 *)

LinearRecurrence[{1, 0, 1, -1}, {1, 4, 5, 7}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 6 in [1, 4, 5]]; // Wesley Ivan Hurt, Jun 11 2016

CROSSREFS

Cf. A144430 (essentially the same), A010882 (first differences), A080341 (partial sums).

Sequence in context: A231575 A335001 A153085 * A287658 A039577 A013951

Adjacent sequences:  A047256 A047257 A047258 * A047260 A047261 A047262

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 30 13:38 EDT 2021. Contains 346359 sequences. (Running on oeis4.)