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A109784 Expansion of (x^2-x-1)*(x^3-x^2+x-2) / ((x-1)*(2*x-1)*(x^2+x+1)*(x^2+1)). 1

%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^2-x-1)*(x^3-x^2+x-2) / ((x-1)*(2*x-1)*(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(n-1) - a(n-2) + 3*a(n-3) - 2*a(n-4) + a(n-5) - 2*a(n-6) 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

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Last modified December 5 06:30 EST 2021. Contains 349532 sequences. (Running on oeis4.)