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

%I

%S 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,

%T 43,44,48,49,50,51,55,56,57,58,62,63,64,65,69,70,71,72,76,77,78,79,83,

%U 84,85,86,90,91,92,93,97,98,99,100,104,105,106,107,111,112

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

%H Daniel Starodubtsev, <a href="/A047279/b047279.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F 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

%F From _Wesley Ivan Hurt_, May 21 2016: (Start)

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

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

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

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

%p 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

%t LinearRecurrence[{1,0,0,1,-1},{0,1,2,6,7},80] (* _Harvey P. Dale_, Jun 15 2015 *)

%o (MAGMA) [n : n in [0..100] | n mod 7 in [0, 1, 2, 6]]; // _Wesley Ivan Hurt_, May 21 2016

%Y Cf. A047322, A047336, A047352, A047361.

%K nonn,easy,changed

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Wesley Ivan Hurt_, May 21 2016

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Last modified May 11 11:54 EDT 2021. Contains 343791 sequences. (Running on oeis4.)