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Expansion of (-3*x^3-18*x^2+14*x-1)/(3*x^4-5*x^2+4*x-1).
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%I #25 Mar 07 2024 16:02:41

%S 1,-10,-27,-55,-82,-83,-3,238,721,1445,2166,2153,-55,-6650,-19827,

%T -39599,-59426,-59659,-987,175550,528857,1058701,1587558,1583377,

%U -17711,-4811626,-14395275,-28772839,-43168114,-43243139,-317811,128625934,386588449,773494709,1160083158,1158736889

%N Expansion of (-3*x^3-18*x^2+14*x-1)/(3*x^4-5*x^2+4*x-1).

%C A floretion-generated sequence which emerges as a transformation of A000004. a(6n+6)= A103134(n).

%C It appears that Fib(6n+1) = a(6n+4) - a(6n+5). - _Creighton Dement_, Jan 31 2005

%C Floretion Algebra Multiplication Program. FAMP code: 4lesforcycseq[ - .25'i + .5'j - .25i' - .5j' + .5k' - .25'ii' + .75'jj' - .25'kk' + .5'ji' + .25'jk' + .25'kj' + .75e ] Note: vesforcycseq = A000004, 4lesforseq gives A000045, vesseq gives A057681.

%H Colin Barker, <a href="/A103135/b103135.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,3).

%F a(n) = -9*A057083(n-1) - Fib(n-2). - _Ralf Stephan_, May 18 2007

%F a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-4) for n>3. - _Colin Barker_, May 06 2019

%o (PARI) Vec((-3*x^3-18*x^2+14*x-1)/(3*x^4-5*x^2+4*x-1)+O(x^99)) \\ _Charles R Greathouse IV_, Feb 05 2013

%Y Cf. A103134.

%K sign,easy

%O 0,2

%A _Creighton Dement_, Jan 24 2005

%E Definition not clear to me. A000004 is the zero sequence! _N. J. A. Sloane_.