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A047275 Numbers that are congruent to {0, 1, 6} mod 7. 2
0, 1, 6, 7, 8, 13, 14, 15, 20, 21, 22, 27, 28, 29, 34, 35, 36, 41, 42, 43, 48, 49, 50, 55, 56, 57, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92, 97, 98, 99, 104, 105, 106, 111, 112, 113, 118, 119, 120, 125, 126, 127, 132, 133, 134, 139, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Nonnegative m such that floor(k*m^2/7) = k*floor(m^2/7), where k = 4, 5 or 6. See also the comment in A047299. [Bruno Berselli, Dec 03 2015]

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

G.f.: x^2*(1+5*x+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

a(n) = (21*n-21+12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

MAPLE

A047275:=n->(21*n-21+12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047275(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

MATHEMATICA

Select[Range[0, 120], Function[k, Mod[#, 7] == k] /@ Or[0, 1, 6] &] (* or *) Select[Range[0, 120], Function[k, Floor[k (#^2/7)] == k Floor[#^2/7]] /@ Or[4, 5, 6] &] (* Michael De Vlieger, Dec 03 2015 *)

LinearRecurrence[{1, 0, 1, -1}, {0, 1, 6, 7}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(PARI) concat(0, Vec(x^2*(1+5*x+x^2)/((1+x+x^2)*(x-1)^2) + O(x^100))) \\ Altug Alkan, Dec 03 2015

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 6]]; // Wesley Ivan Hurt, Jun 10 2016

CROSSREFS

Cf. A047299.

Sequence in context: A037365 A083340 A118733 * A327301 A047590 A146329

Adjacent sequences:  A047272 A047273 A047274 * A047276 A047277 A047278

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)