A047384 Numbers that are congruent to {0, 1, 5} mod 7.

0, 1, 5, 7, 8, 12, 14, 15, 19, 21, 22, 26, 28, 29, 33, 35, 36, 40, 42, 43, 47, 49, 50, 54, 56, 57, 61, 63, 64, 68, 70, 71, 75, 77, 78, 82, 84, 85, 89, 91, 92, 96, 98, 99, 103, 105, 106, 110, 112, 113, 117, 119, 120, 124, 126, 127, 131, 133, 134, 138, 140

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

G.f.: x^2*(1+4*x+2*x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

a(n) = Sum_{i=0..n-2} 2^(-i mod 3). - Wesley Ivan Hurt, Jul 08 2014

a(n) = 3 + floor((n-2)/3) + 2*floor((n-4)/3) + 4*floor(n/3). - Wesley Ivan Hurt, Jul 13 2014

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-24+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047384:=n->3 + floor((n-2)/3) + 2*floor((n-4)/3) + 4*floor(n/3): seq(A047384(n), n=1..50); # Wesley Ivan Hurt, Jul 13 2014

Mathematica

CoefficientList[Series[x*(1 + 4*x + 2*x^2)/((1 + x + x^2)*(x - 1)^2), {x, 0, 50}], x] (* or *) Table[3 + Floor[(n - 2)/3] + 2*Floor[(n - 4)/3] + 4*Floor[n/3], {n, 50}] (* Wesley Ivan Hurt, Jul 08 2014 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 5, 7}, 90] (* Harvey P. Dale, May 26 2017 *)
Select[Range[0, 150], MemberQ[{0, 1, 5}, Mod[#, 7]] &] (* Vincenzo Librandi, May 27 2017 *)

Prog

(Magma) [3 + Floor((n-2)/3) + 2*Floor((n-4)/3) + 4*Floor(n/3) : n in [1..50]]; // Wesley Ivan Hurt, Jul 13 2014
(Magma) &cat[[n, n+1, n+5]: n in [0..150 by 7]]; // Vincenzo Librandi, May 27 2017

Crossrefs

Sequence in context: A061813 A173664 A171420 * A257772 A356897 A314374

Adjacent sequences: A047381 A047382 A047383 * A047385 A047386 A047387

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved