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A047312 Numbers that are congruent to {0, 4, 5, 6} mod 7.

%I A047312 #17 Sep 08 2022 08:44:56
%S A047312 0,4,5,6,7,11,12,13,14,18,19,20,21,25,26,27,28,32,33,34,35,39,40,41,
%T A047312 42,46,47,48,49,53,54,55,56,60,61,62,63,67,68,69,70,74,75,76,77,81,82,
%U A047312 83,84,88,89,90,91,95,96,97,98,102,103,104,105,109,110,111
%N A047312 Numbers that are congruent to {0, 4, 5, 6} mod 7.
%H A047312 Daniel Starodubtsev, <a href="/A047312/b047312.txt">Table of n, a(n) for n = 1..10000</a>
%H A047312 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047312 G.f.: x^2*(4+x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F A047312 From _Wesley Ivan Hurt_, Jun 03 2016: (Start)
%F A047312 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047312 a(n) = (14*n-5+3*i^(2*n)-(3+3*i)*i^(-n)-(3-3*i)*i^n)/8 where i=sqrt(-1).
%F A047312 a(2k) = A047288(k), a(2k-1) = A047382(k). (End)
%p A047312 A047312:=n->(14*n-5+3*I^(2*n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8: seq(A047312(n), n=1..100); # _Wesley Ivan Hurt_, Jun 03 2016
%t A047312 Table[(14n-5+3*I^(2n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 03 2016 *)
%o A047312 (Magma) [n : n in [0..150] | n mod 7 in [0, 4, 5, 6]]; // _Wesley Ivan Hurt_, Jun 03 2016
%Y A047312 Cf. A047288, A047382.
%K A047312 nonn,easy
%O A047312 1,2
%A A047312 _N. J. A. Sloane_