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A047331 Numbers that are congruent to {2, 3, 5, 6} mod 7.

%I A047331 #13 Sep 08 2022 08:44:57
%S A047331 2,3,5,6,9,10,12,13,16,17,19,20,23,24,26,27,30,31,33,34,37,38,40,41,
%T A047331 44,45,47,48,51,52,54,55,58,59,61,62,65,66,68,69,72,73,75,76,79,80,82,
%U A047331 83,86,87,89,90,93,94,96,97,100,101,103,104,107,108,110,111
%N A047331 Numbers that are congruent to {2, 3, 5, 6} mod 7.
%H A047331 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047331 G.f.: x*(2+x+2*x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F A047331 From _Wesley Ivan Hurt_, Jun 03 2016: (Start)
%F A047331 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047331 a(n) = (14*n-3-3*i^(2*n)-(1-i)*i^(-n)-(1+i)*i^n)/8 where i=sqrt(-1).
%F A047331 a(2k) = A047280(k), a(2k-1) = A047385(k). (End)
%p A047331 A047331:=n->(14*n-3-3*I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/8: seq(A047331(n), n=1..100); # _Wesley Ivan Hurt_, Jun 03 2016
%t A047331 Table[(14n-3-3*I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 03 2016 *)
%o A047331 (Magma) [n : n in [0..150] | n mod 7 in [2, 3, 5, 6]]; // _Wesley Ivan Hurt_, Jun 03 2016
%Y A047331 Cf. A047280, A047385.
%K A047331 nonn,easy
%O A047331 1,1
%A A047331 _N. J. A. Sloane_