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A273182 a(n) is the second number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of a magic square of squares. 4

%I

%S 14,84,490,2856,16646,97020,565474,3295824,19209470,111960996,

%T 652556506,3803378040,22167711734,129202892364,753049642450,

%U 4389094962336,25581520131566,149100025827060,869018634830794,5065011783157704,29521052064115430,172061300601534876

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

%C The multiplying factor 6 appears to come from the ratio of a(1)/a(0) of the sequence. Each of the lines of tables (V vs VII) or (VI vs VIII) in oddwheel.com/ImaginaryB.html generates this factor.

%H Colin Barker, <a href="/A273182/b273182.txt">Table of n, a(n) for n = 0..1000</a>

%H E. Gutierrez,<a href="http://www.oddwheel.com/ImaginaryF6.html">Recursion Methods to Generate New Integer Sequences (Part VIF)</a>

%H 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 E. Gutierrez, <a href="http://www.oddwheel.com/ImaginaryC.html">Table of Tuples for Square of Squares (Part IC)</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).

%F a(0)=14, a(1)= 84, a(n+1)= a(n)*6 - a(n-1).

%F G.f.: 14 / (1-6*x+x^2). - _Colin Barker_, May 18 2016

%F E.g.f.: 7*(3*sqrt(2)*sinh(2*sqrt(2)*x) + 4*cosh(2*sqrt(2)*x))*exp(3*x)/2. - _Ilya Gutkovskiy_, May 18 2016

%e a(2) = 84*6 -14 = 490; a(3) = 490*6 - 84 = 2856; a(4) = 2856*6 - 490 = 16646.

%t CoefficientList[Series[14/(1 - 6 x + x^2), {x, 0, 21}], x] (* _Michael De Vlieger_, May 18 2016 *)

%o (PARI) Vec(14/(1-6*x+x^2) + O(x^50)) \\ _Colin Barker_, May 18 2016

%Y Cf. A178218, A273187, A273189.

%K nonn,easy

%O 0,1

%A _Eddie Gutierrez_, May 17 2016

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Last modified February 22 23:03 EST 2019. Contains 320411 sequences. (Running on oeis4.)