A047279 Numbers that are congruent to {0, 1, 2, 6} mod 7.

0, 1, 2, 6, 7, 8, 9, 13, 14, 15, 16, 20, 21, 22, 23, 27, 28, 29, 30, 34, 35, 36, 37, 41, 42, 43, 44, 48, 49, 50, 51, 55, 56, 57, 58, 62, 63, 64, 65, 69, 70, 71, 72, 76, 77, 78, 79, 83, 84, 85, 86, 90, 91, 92, 93, 97, 98, 99, 100, 104, 105, 106, 107, 111, 112

Offset

1,3

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

Formula

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

From Wesley Ivan Hurt, May 21 2016: (Start)

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

a(n) = (14n-17+3*(i^(2n)+(1+i)*i^(-n)+(1-i)*i^n))/8 where i = sqrt(-1).

a(2n) = A047336(n), a(2n-1) = A047352(n).

a(n) = A047361(n+1) - 1. a(2-n) = - A047322(n). (End)

Maple

A047279:=n->(14*n-17+3*(I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n))/8: seq(A047279(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 6, 7}, 80] (* Harvey P. Dale, Jun 15 2015 *)

Prog

(Magma) [n : n in [0..100] | n mod 7 in [0, 1, 2, 6]]; // Wesley Ivan Hurt, May 21 2016

Crossrefs

Cf. A047322, A047336, A047352, A047361.

Sequence in context: A243652 A080780 A138168 * A162917 A250183 A260139

Adjacent sequences: A047276 A047277 A047278 * A047280 A047281 A047282

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 21 2016

Status

approved