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%I #9 Mar 05 2024 05:07:30
%S 28,476,1106,8218,18256,131600,291578,2097970,4647580,33436508,
%T 74070290,532886746,1180477648,8492752016,18813572666,135351146098,
%U 299836685596,2157125586140,4778573397458,34378658232730,76157337674320,547901406138128,1213738829392250
%N Positive integers n such that (n+84)^3 - n^3 is a square.
%H Colin Barker, <a href="/A263949/b263949.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,16,-16,-1,1).
%F a(n) = a(n-1)+16*a(n-2)-16*a(n-3)-a(n-4)+a(n-5) for n>5.
%F G.f.: 14*x*(x^4+4*x^3-13*x^2-32*x-2) / ((x-1)*(x^4-16*x^2+1)).
%e 28 is in the sequence because (28+84)^3 - 28^3 = 1176^2.
%t LinearRecurrence[{1, 16, -16, -1, 1}, {28, 476, 1106, 8218, 18256}, 30] (* _Paolo Xausa_, Mar 05 2024 *)
%o (PARI) Vec(14*x*(x^4+4*x^3-13*x^2-32*x-2)/((x-1)*(x^4-16*x^2+1)) + O(x^40))
%Y Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263948 (61) 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
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