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%I #23 Sep 08 2022 08:44:57
%S 0,1,3,5,7,8,10,12,14,15,17,19,21,22,24,26,28,29,31,33,35,36,38,40,42,
%T 43,45,47,49,50,52,54,56,57,59,61,63,64,66,68,70,71,73,75,77,78,80,82,
%U 84,85,87,89,91,92,94,96,98,99,101,103,105,106,108,110
%N Numbers that are congruent to {0, 1, 3, 5} 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+2*x^2+2*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 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) = (14*n - 17 - i^(2*n) + (1 + i)*i^(-n) + (1 - i)*i^n)/8.
%F a(2k) = A047383(k), a(2k-1) = A047355(k). (End)
%F a(n) = n + floor(3*n/4-3/4) - 1. - _Bruno Berselli_, Jun 15 2016
%p A047392:=n->(14*n-17-I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n)/8: seq(A047392(n), n=1..100); # _Wesley Ivan Hurt_, May 21 2016
%t Table[(14n-17-I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 21 2016 *)
%t Table[n + Floor[3 n/4 - 3/4] - 1, {n, 1, 70}] (* _Bruno Berselli_, Jun 15 2016 *)
%o (Magma) [n: n in [0..100] | n mod 7 in [0, 1, 3, 5]]; // _Wesley Ivan Hurt_, May 21 2016
%Y Cf. A047355, A047383.
%Y Cf. A047371: n + floor(3*n/4-1/2) - 1; A047379: n + floor(3*n/4-1/4) - 1.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Wesley Ivan Hurt_, May 21 2016
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