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A047278 Numbers that are congruent to {1, 2, 6} mod 7. 2
1, 2, 6, 8, 9, 13, 15, 16, 20, 22, 23, 27, 29, 30, 34, 36, 37, 41, 43, 44, 48, 50, 51, 55, 57, 58, 62, 64, 65, 69, 71, 72, 76, 78, 79, 83, 85, 86, 90, 92, 93, 97, 99, 100, 104, 106, 107, 111, 113, 114, 118, 120, 121, 125, 127, 128, 132, 134, 135, 139, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..61.

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

FORMULA

G.f.: x*(1+x+4*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)

MAPLE

A047278:=n->(21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047278(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

MATHEMATICA

Table[(21*n-15+6*Cos[2*n*Pi/3]+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n,

80}] (* Wesley Ivan Hurt, Jun 07 2016 *)

Select[Range[200], MemberQ[{1, 2, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 2, 6, 8}, 100] (* Harvey P. Dale, Dec 16 2018 *)

PROG

(MAGMA) [n : n in [1..150] | n mod 7 in [1, 2, 6]]; // Wesley Ivan Hurt, Jun 07 2016

CROSSREFS

Sequence in context: A262981 A336745 A034591 * A242204 A172209 A107737

Adjacent sequences:  A047275 A047276 A047277 * A047279 A047280 A047281

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)