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%I #30 Mar 19 2024 11:48:51
%S 1,30,929,28769,890910,27589441,854381761,26458245150,819351217889,
%T 25373429509409,785756963573790,24333092441278081,753540108716046721,
%U 23335410277756170270,722644178501725231649,22378634123275726010849,693015013643045781104670
%N a(n) = 31*a(n-1)-a(n-2).
%C Take 31 numbers consisting of 29 ones together with any two successive terms from this sequence. This set has the property that the sum of their squares is 31 times their product. (Guy)
%C Positive values of x (or y) satisfying x^2 - 31xy + y^2 + 29 = 0. - _Colin Barker_, Feb 24 2014
%H Vincenzo Librandi, <a href="/A111216/b111216.txt">Table of n, a(n) for n = 0..200</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (31,-1).
%F G.f.: (1-x)/(1-31*x+x^2). [_Philippe Deléham_, Nov 18 2008]
%F a(n) = A200442(n) - A200442(n-1). - _R. J. Mathar_, Feb 13 2016
%t CoefficientList[Series[(1 - x)/(1 - 31 x + x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 26 2014 *)
%o (PARI) Vec((1-x)/(1-31*x+x^2) + O(x^100)) \\ _Colin Barker_, Feb 24 2014
%o (Magma) I:=[1,30]; [n le 2 select I[n] else 31*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Feb 26 2014
%Y Cf. A049685.
%Y Cf. similar sequences listed in A238379.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, following a suggestion from _R. K. Guy_, Oct 26 2005
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