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%I #12 Feb 17 2017 17:07:26
%S 1,6,28,144,688,3360,16192,78336,378112,1826304,8817664,42577920,
%T 205582336,992649216,4792926208,23142334464,111741042688,539533639680,
%U 2605098729472,12578530000896,60734514921472,293252181786624,1415946786832384,6836795882864640
%N Expansion of (1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
%C Note (see program code): ibaseseq[A*B] = A057087, basejseq[A*B] = A099582, tesseq[A*B] = A110046.
%H Matthew House, <a href="/A110047/b110047.txt">Table of n, a(n) for n = 0..1454</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 a(n) = 4*a(n-1) + 8*a(n-2) - 16*a(n-3) - 16*a(n-4). - _Matthew House_, Feb 17 2017
%F a(n) = (-3*(2-2*sqrt(2))^n*(-2+sqrt(2)) + 2^n*(-2*(1+(-1)^n)+3*(1+sqrt(2))^n*(2+sqrt(2)))) / 8. - _Colin Barker_, Feb 17 2017
%p seriestolist(series((1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -kbasekseq[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 + 2 x - 4 x^2)/((2 x + 1)(2 x - 1)(4 x^2 + 4 x - 1)), {x, 0, 21}], x] (* or *)
%t LinearRecurrence[{4, 8, -16, -16}, {1, 6, 28, 144}, 22] (* _Michael De Vlieger_, Feb 17 2017 *)
%o (PARI) Vec((1+2*x-4*x^2) / ((2*x+1)*(2*x-1)*(4*x^2+4*x-1)) + O(x^30)) \\ _Colin Barker_, Feb 17 2017
%Y Cf. A110046, A110048, A110049.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Jul 10 2005
%E Definition corrected by _Matthew House_, Feb 17 2017
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