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A047379 Numbers that are congruent to {0, 2, 4, 5} mod 7.

%I A047379 #22 Sep 08 2022 08:44:57
%S A047379 0,2,4,5,7,9,11,12,14,16,18,19,21,23,25,26,28,30,32,33,35,37,39,40,42,
%T A047379 44,46,47,49,51,53,54,56,58,60,61,63,65,67,68,70,72,74,75,77,79,81,82,
%U A047379 84,86,88,89,91,93,95,96
%N A047379 Numbers that are congruent to {0, 2, 4, 5} mod 7.
%H A047379 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047379 a(n) = floor(floor((7n + 2)/2)/2).
%F A047379 a(n) = floor((7n-5)/4). - _Gary Detlefs_, Mar 07 2010
%F A047379 G.f.: x^2*(2+2*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F A047379 From _Wesley Ivan Hurt_, Dec 03 2014: (Start)
%F A047379 a(n) = a(n-1) + a(n-4) - a(n-5), n>5;
%F A047379 a(n) = (14*n-13-(-1)^n+2*i^n*(-1)^((3+(-1)^n)/4))/8, where i = sqrt(-1);
%F A047379 a(n) = A047215(n-1) - A057353(n-1). (End)
%p A047379 A047379:=n->floor((7*n-5)/4): seq(A047379(n), n=1..100); # _Wesley Ivan Hurt_, Dec 03 2014
%t A047379 Select[Range[0,100],MemberQ[{0,2,4,5},Mod[#,7]]&] (* _Harvey P. Dale_, Apr 10 2014 *)
%o A047379 (Magma) [Floor((7*n-5)/4) : n in [1..100]]; // _Wesley Ivan Hurt_, Dec 03 2014
%Y A047379 Cf. A047215, A057353.
%K A047379 nonn,easy
%O A047379 1,2
%A A047379 _N. J. A. Sloane_