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%I #24 Jul 18 2016 05:52:48
%S 49,5341,587461,64615369,7107103129,781716728821,85981733067181,
%T 9457208920661089,1040206999539652609,114413312740441125901,
%U 12584424194448984196501,1384172248076647820489209,152246362864236811269616489,16745715742817972591837324581
%N Values of k arising in A144927.
%C Numbers k such that there exists x in N : (x+7)^3-x^3=k^2. - _Richard Choulet_, Oct 16 2008
%H Colin Barker, <a href="/A144928/b144928.txt">Table of n, a(n) for n = 1..450</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110,-1).
%F a(n+2) = 110*a(n+1)-a(n). - _Richard Choulet_, Oct 16 2008
%F G.f.: 49*x*(1-x) / (1-110*x+x^2). - _Colin Barker_, Oct 17 2014, corrected Jul 16 2016
%e a(1) = 49 because (7+7)^3 - 7^3 = 2041 = 49^2. - _Richard Choulet_, Oct 16 2008
%e a(2) = 5341 because (1162+7)^3 - 1162^3 = 28526281 = 5341^2. - _Colin Barker_, Jul 16 2016
%t Sqrt[(# + 7)^3 - #^3] & /@ Rest@ CoefficientList[Series[7 x (-1 - 55 x + 2 x^2)/((x - 1) (x^2 - 110 x + 1)), {x, 0, 14}], x] (* or *)
%t Rest@ CoefficientList[Series[49 x (1 - x)/(1 - 110 x + x^2), {x, 0, 14}], x] (* _Michael De Vlieger_, Jul 17 2016 *)
%o (PARI) Vec(49*x*(1-x)/(1-110*x+x^2) + O(x^20)) \\ _Colin Barker_, Oct 17 2014, corrected Jul 16 2016
%Y Cf. A144927.
%K nonn,easy
%O 1,1
%A _Richard Choulet_, Sep 25 2008
%E More terms from _Colin Barker_, Oct 17 2014
%E All terms except the first corrected by _Colin Barker_, Jul 16 2016
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