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A047283 Numbers that are congruent to {0, 1, 3, 6} mod 7. 2

%I

%S 0,1,3,6,7,8,10,13,14,15,17,20,21,22,24,27,28,29,31,34,35,36,38,41,42,

%T 43,45,48,49,50,52,55,56,57,59,62,63,64,66,69,70,71,73,76,77,78,80,83,

%U 84,85,87,90,91,92,94,97,98,99,101,104,105,106,108,111

%N Numbers that are congruent to {0, 1, 3, 6} mod 7.

%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+2*x+3*x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - _Harvey P. Dale_, Mar 09 2012

%F From _Wesley Ivan Hurt_, May 22 2016: (Start)

%F a(n) = (14n-15+i^(2n)+(3+i)*i^(-n)+(3-i)*i^n)/8 where i=sqrt(-1).

%F a(2n) = A047336(n), a(2n-1) = A047355(n). (End)

%p A047283:=n->(14*n-15+I^(2*n)+(3+I)*I^(-n)+(3-I)*I^n)/8: seq(A047283(n), n=1..100); # _Wesley Ivan Hurt_, May 22 2016

%t Select[Range[0,100], MemberQ[{0,1,3,6}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {0,1,3,6,7}, 60] (* _Harvey P. Dale_, Mar 09 2012 *)

%o (MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 3, 6]]; // _Wesley Ivan Hurt_, May 22 2016

%Y Cf. A047336, A047355.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Wesley Ivan Hurt_, May 22 2016

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)