A047357 Numbers that are congruent to {0, 1, 3} mod 7.

0, 1, 3, 7, 8, 10, 14, 15, 17, 21, 22, 24, 28, 29, 31, 35, 36, 38, 42, 43, 45, 49, 50, 52, 56, 57, 59, 63, 64, 66, 70, 71, 73, 77, 78, 80, 84, 85, 87, 91, 92, 94, 98, 99, 101, 105, 106, 108, 112, 113, 115, 119, 120, 122, 126, 127, 129, 133, 134, 136, 140

Offset

1,3

Links

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

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

Formula

Partial sums of (0, 1, 2, 4, 1, 2, 4, 1, 2, 4, ...). - Gary W. Adamson, Jun 19 2008

G.f.: x^2*(1+2*x+4*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 08 2016: (Start)

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

a(n) = (21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-4, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End)

Maple

A047357:=n->(21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047357(n), n=1..100); # Wesley Ivan Hurt, Jun 08 2016

Mathematica

Select[Range[0, 200], Mod[#, 7] == 0 || Mod[#, 7] == 1 || Mod[#, 7] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *)
Select[Range[0, 200], MemberQ[{0, 1, 3}, Mod[#, 7]]&] (* Harvey P. Dale, Nov 30 2012 *)
Accumulate[PadRight[{0}, 70, {4, 1, 2}]] (* Harvey P. Dale, Aug 16 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 3]]; // Wesley Ivan Hurt, Jun 08 2016

Crossrefs

Cf. A047360.

Sequence in context: A276002 A089970 A019270 * A003607 A087859 A300082

Adjacent sequences: A047354 A047355 A047356 * A047358 A047359 A047360

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved