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%I #36 Sep 08 2022 08:45:49
%S 3,10,10,17,17,24,24,31,31,38,38,45,45,52,52,59,59,66,66,73,73,80,80,
%T 87,87,94,94,101,101,108,108,115,115,122,122,129,129,136,136,143,143,
%U 150,150,157,157,164,164,171,171,178,178,185,185,192,192,199,199,206,206
%N a(n) = (5 + 14*n + 7*(-1)^n)/4.
%C Essentially the same as A168376.
%H Vincenzo Librandi, <a href="/A168331/b168331.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 7*n - a(n-1) - 1, with n > 1, a(1)=3.
%F G.f.: x*(3+7*x-3*x^2) / ((1+x)*(x-1)^2). - _R. J. Mathar_, Jan 05 2011
%F a(1)=3, a(2)=10, a(3)=10; for n>3, a(n) = a(n-1)+a(n-2)-a(n-3). - _Harvey P. Dale_, Oct 24 2011
%F E.g.f.: (1/4)*(7 - 12*exp(x) + (5 + 14*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 18 2016
%p A168331:=n->(5+14*n+7*(-1)^n)/4: seq(A168331(n), n=1..100); # _Wesley Ivan Hurt_, May 03 2017
%t Table[5/4 + 7n/2 + 7 (-1)^n/4, {n,60}] (* or *) LinearRecurrence[{1, 1, -1}, {3, 10, 10}, 60] (* _Harvey P. Dale_, Oct 24 2011 *)
%t CoefficientList[Series[- (- 3 - 7 x + 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 17 2013 *)
%o (Magma) [5/4+7*n/2+7*(-1)^n/4: n in [1..70]]; // _Vincenzo Librandi_, Sep 17 2013
%Y Cf. A017017, A168376.
%K nonn,easy,less
%O 1,1
%A _Vincenzo Librandi_, Nov 23 2009
%E New definition by _R. J. Mathar_, Jan 05 2011
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