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.

14, 84, 490, 2856, 16646, 97020, 565474, 3295824, 19209470, 111960996, 652556506, 3803378040, 22167711734, 129202892364, 753049642450, 4389094962336, 25581520131566, 149100025827060, 869018634830794, 5065011783157704, 29521052064115430, 172061300601534876

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, Recursion Methods to Generate New Integer Sequences (Part VIF)

E. Gutierrez, Table of Tuples and Use of Magic Ratio for Tuple Conversion (Part IB)

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