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%I #18 Mar 11 2024 23:13:27
%S 1,49,841,11881,165649,2307361,32137561,447618649,6234523681,
%T 86835713041,1209465459049,16845680713801,234630064534321,
%U 3267975222766849,45517023054201721,633970347536057401
%N Expansion of (1 +34*x +121*x^2)/((1-x)*(x^2 -14*x +1)).
%C A floretion-generated sequence of squares.
%C Floretion Algebra Multiplication Program, FAMP Code: 1vescycseq[C*B] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' B = - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj'
%H G. C. Greubel, <a href="/A110906/b110906.txt">Table of n, a(n) for n = 0..870</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).
%F a(n) = -13 + 14*A007655(n+2) - 134*A007655(n+1). - _R. J. Mathar_, Nov 10 2009
%F From _Colin Barker_, May 06 2019: (Start)
%F a(n) = -13 + (7-4*sqrt(3))^n*(7+(3*sqrt(3))/2) + (7-(3*sqrt(3))/2)*(7+4*sqrt(3))^n.
%F a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3) for n>2. (End)
%t CoefficientList[Series[(1 + 34*x + 121*x^2)/((1 - x)*(x^2 - 14*x + 1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 19 2017 *)
%o (PARI) x='x+O('x^50); Vec((1 +34*x +121*x^2)/((1-x)*(x^2 -14*x +1))) \\ _G. C. Greubel_, Oct 19 2017
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Sep 21 2005
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