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%I #11 May 01 2019 09:10:38
%S 1,8,28,144,656,3200,15296,73984,356608,1722368,8313856,40144896,
%T 193826816,935886848,4518821888,21818834944,105350496256,508677324800,
%U 2456110759936,11859152338944,57261050298368,276480810549248
%N Expansion of (1+4*x-12*x^2-16*x^3)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
%H Colin Barker, <a href="/A110046/b110046.txt">Table of n, a(n) for n = 0..1000</a>
%H Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-floretion.html">Sequences Related to Floretions</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, 8, -16, -16).
%F From _Colin Barker_, May 01 2019: (Start)
%F a(n) = ((2 - 2*sqrt(2))^(1+n) + 2*(-(-2)^n + 2^n + 2^n*(1+sqrt(2))^(1+n))) / 4.
%F a(n) = 4*a(n-1) + 8*a(n-2) - 16*a(n-3) - 16*a(n-4) for n>3.
%F (End)
%p seriestolist(series((1+4*x-12*x^2-16*x^3)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tesseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'
%t CoefficientList[Series[(1+4x-12x^2-16x^3)/((2x+1)(2x-1)(4x^2+4x-1)),{x,0,40}],x] (* or *) LinearRecurrence[{4,8,-16,-16},{1,8,28,144},40] (* _Harvey P. Dale_, Jun 12 2016 *)
%o (PARI) Vec((1 + 4*x - 12*x^2 - 16*x^3) / ((1 - 2*x)*(1 + 2*x)*(1 - 4*x - 4*x^2)) + O(x^40)) \\ _Colin Barker_, May 01 2019
%Y Cf. A110047, A110048, A110049, A110050.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Jul 10 2005
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