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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
 14, 84, 490, 2856, 16646, 97020, 565474, 3295824, 19209470, 111960996, 652556506, 3803378040, 22167711734, 129202892364, 753049642450, 4389094962336, 25581520131566, 149100025827060, 869018634830794, 5065011783157704, 29521052064115430, 172061300601534876 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5. E. Gutierrez, Table of Tuples for Square of Squares (Part IC) Index entries for linear recurrences with constant coefficients, signature (6,-1). FORMULA a(0)=14, a(1)= 84, a(n+1)= a(n)*6 - a(n-1). G.f.: 14 / (1-6*x+x^2). - Colin Barker, May 18 2016 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 EXAMPLE a(2) = 84*6 -14 = 490; a(3) = 490*6 - 84 = 2856; a(4) = 2856*6 - 490 = 16646. MATHEMATICA CoefficientList[Series[14/(1 - 6 x + x^2), {x, 0, 21}], x] (* Michael De Vlieger, May 18 2016 *) PROG (PARI) Vec(14/(1-6*x+x^2) + O(x^50)) \\ Colin Barker, May 18 2016 CROSSREFS Cf. A178218, A273187, A273189. Sequence in context: A006858 A027818 A054149 * A341854 A025607 A272103 Adjacent sequences: A273179 A273180 A273181 * A273183 A273184 A273185 KEYWORD nonn,easy AUTHOR Eddie Gutierrez, May 17 2016 STATUS approved

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Last modified December 6 09:17 EST 2022. Contains 358606 sequences. (Running on oeis4.)