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A273187 a(n) is the third number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of magic square of squares.

%I A273187 #23 Jun 07 2016 12:02:54
%S A273187 99,449,2499,14449,84099,490049,2856099,16646449,97022499,565488449,
%T A273187 3295908099,19209960049,111963852099,652573152449,3803475062499,
%U A273187 22168277222449,129206188272099,753068852410049,4389206926188099,25582172704718449,149103829302122499
%N A273187 a(n) is the third number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of magic square of squares.
%H A273187 Colin Barker, <a href="/A273187/b273187.txt">Table of n, a(n) for n = 0..1000</a>
%H A273187 E. Gutierrez, <a href="http://www.oddwheel.com/ImaginaryF6.html">Recursion Methods to Generate New Integer Sequences (Part VIF)</a>
%H A273187 E. Gutierrez, <a href="http://www.oddwheel.com/ImaginaryB.html">Table of Tuples and Use of Magic Ratio for Tuple Conversion (Part IB)</a>
%H A273187 E. Gutierrez, <a href="http://www.oddwheel.com/ImaginaryC.html">Table of Tuples for Square of Squares (Part IC)</a>
%H A273187 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A273187 a(0)= 99, a(1)= 449, a(n+1)= a(n)*6 - a(n-1) - k where k=96.
%F A273187 From _Colin Barker_, May 18 2016: (Start)
%F A273187 a(n) = (24+25/2*(3-2*sqrt(2))^(1+n)+25/2*(3+2*sqrt(2))^(1+n)).
%F A273187 a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>2.
%F A273187 G.f.: (99-244*x+49*x^2) / ((1-x)*(1-6*x+x^2)).
%F A273187 (End)
%F A273187 a(n) = 24 + 25*A001541(n+1). - _R. J. Mathar_, Jun 07 2016
%e A273187 a(2)= 449*6 - (99 + 96)= 2499;
%e A273187 a(3)= 2499*6 - (449 + 96)= 14449.
%t A273187 CoefficientList[Series[(99 - 244 x + 49 x^2)/((1 - x) (1 - 6 x + x^2)), {x, 0, 20}], x] (* _Michael De Vlieger_, May 20 2016 *)
%o A273187 (PARI) Vec((99-244*x+49*x^2)/((1-x)*(1-6*x+x^2)) + O(x^50)) \\ _Colin Barker_, May 18 2016
%Y A273187 Cf. A273182, A273189.
%K A273187 nonn,easy
%O A273187 0,1
%A A273187 _Eddie Gutierrez_, May 17 2016