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%I #11 Feb 05 2019 13:38:28
%S 26,2626,132522,6624722,331104826,16548617826,827099787722,
%T 41338440769522,2066094938689626,103263408493713026,
%U 5161104329746962922,257951953078854434322,12892436549612974754426,644363875527569883288226,32205301339828881189658122
%N Positive integers n such that (n+52)^3 - n^3 is a square.
%H Colin Barker, <a href="/A263946/b263946.txt">Table of n, a(n) for n = 1..588</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (51,-51,1).
%F a(n) = 51*a(n-1)-51*a(n-2)+a(n-3) for n>3.
%F G.f.: 26*x*(3*x^2-50*x-1) / ((x-1)*(x^2-50*x+1)).
%F a(n) = 26*(-6-(6+sqrt(39))*(25+4*sqrt(39))^(-n)+(-6+sqrt(39))*(25+4*sqrt(39))^n)/6. - _Colin Barker_, Mar 03 2016
%e 26 is in the sequence because (26+52)^3 - 26^3 = 676^2.
%t LinearRecurrence[{51,-51,1},{26,2626,132522},20] (* _Harvey P. Dale_, Feb 05 2019 *)
%o (PARI) Vec(26*x*(3*x^2-50*x-1)/((x-1)*(x^2-50*x+1)) + O(x^30))
%Y Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), 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