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A047288 Numbers that are congruent to {4, 6} mod 7.

%I A047288 #34 Sep 21 2022 18:33:21
%S A047288 4,6,11,13,18,20,25,27,32,34,39,41,46,48,53,55,60,62,67,69,74,76,81,
%T A047288 83,88,90,95,97,102,104,109,111,116,118,123,125,130,132,137,139,144,
%U A047288 146,151,153,158,160,165,167,172
%N A047288 Numbers that are congruent to {4, 6} mod 7.
%H A047288 David Lovler, <a href="/A047288/b047288.txt">Table of n, a(n) for n = 1..1000</a>
%H A047288 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047288 a(n) = 7*n - a(n-1) - 4 with n > 1, a(1)=4. - _Vincenzo Librandi_, Aug 05 2010
%F A047288 From _Colin Barker_, Mar 13 2012: (Start)
%F A047288 a(n) = a(n-1) + a(n-2) - a(n-3).
%F A047288 G.f.: x*(4 + 2*x + x^2)/((1-x)^2*(1+x)). (End)
%F A047288 a(n) = (-1 - 3*(-1)^n + 14*n)/4. - _Colin Barker_, May 14 2012
%F A047288 a(n) = floor(7*n/2) - (-1)^n. - _Wesley Ivan Hurt_, Sep 12 2017
%F A047288 E.g.f.: 1 + ((14*x - 1)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Sep 15 2022
%t A047288 LinearRecurrence[{1,1,-1},{4,6,11},50] (* _Harvey P. Dale_, Jan 18 2013 *)
%o A047288 (PARI) a(n) = (-1 - 3*(-1)^n + 14*n)/4 \\ _David Lovler_, Sep 15 2022
%K A047288 nonn,easy
%O A047288 1,1
%A A047288 _N. J. A. Sloane_