%I
%S 2,5,6,14,31,59,118,238,475,951,1902,3802,7607,15215,30426,60854,
%T 121711,243419,486838,973678,1947355,3894711,7789422,15578842,
%U 31157687,62315375,124630746,249261494,498522991,997045979,1994091958,3988183918
%N Expansion of (x^2x1)*(x^3x^2+x2) / ((x1)*(2*x1)*(x^2+x+1)*(x^2+1)).
%H Colin Barker, <a href="/A109784/b109784.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,3,2,1,2).
%F a(n) = 2*a(n1)  a(n2) + 3*a(n3)  2*a(n4) + a(n5)  2*a(n6) for n>5.  _Colin Barker_, May 15 2019
%t LinearRecurrence[{2,1,3,2,1,2},{2,5,6,14,31,59},40] (* _Harvey P. Dale_, Nov 28 2019 *)
%o Floretion Algebra Multiplication Program, 2ibasesumseq[5'i + .5i' + .5'ii' + .5'jj' + .5'kk' + .5e], sumtype: default (ver. f). Note: Due to FAMP's limited ability to handle large numbers, it is unclear if 2ibasesumseq and (a(n)) continue to coincide for large n.
%o (PARI) Vec((1 + x  x^2)*(2  x + x^2  x^3) / ((1  x)*(1  2*x)*(1 + x^2)*(1 + x + x^2)) + O(x^40)) \\ _Colin Barker_, May 15 2019
%K nonn,easy
%O 0,1
%A _Creighton Dement_, Aug 14 2005
