%I #11 Dec 14 2016 13:56:28
%S 28,189,959,4648,22323,107009,512764,2456853,11771543,56400904,
%T 270233019,1294764233,6203588188,29723176749,142412295599,
%U 682338301288,3269279210883,15664057753169,75051009555004,359590990021893,1722903940554503,8254928712750664
%N Positive integers n such that (n+28)^3 - n^3 is a square.
%H Colin Barker, <a href="/A263944/b263944.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 (6,-6,1).
%F a(n) = 6*a(n-1)-6*a(n-2)+a(n-3) for n>3.
%F G.f.: 7*x*(x-4)*(x+1) / ((x-1)*(x^2-5*x+1)).
%F a(n) = 7*(-2+(2^(-1-n)*((5-sqrt(21))^n*(-7+sqrt(21))+(5+sqrt(21))^n*(7+sqrt(21))))/sqrt(21)). - _Colin Barker_, Mar 05 2016
%e 189 is in the sequence because (189+28)^3 - 189^3 = 1862^2.
%t LinearRecurrence[{6,-6,1},{28,189,959},30] (* _Harvey P. Dale_, Dec 14 2016 *)
%o (PARI) Vec(7*x*(x-4)*(x+1)/((x-1)*(x^2-5*x+1)) + O(x^40))
%Y Cf. A263942 (4), A263943 (21), A263945 (39), A263946 (52), A263947 (57), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Oct 30 2015