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A177825 Expansion of 1/((1 + x^3 - x^4)*(1 - x)). 1

%I #25 Jan 22 2019 03:12:41

%S 1,1,1,0,1,1,2,0,1,0,3,0,2,-2,4,-1,5,-5,6,-5,11,-10,12,-15,22,-21,28,

%T -36,44,-48,65,-79,93,-112,145,-171,206,-256,317,-376,463,-572,694,

%U -838,1036,-1265,1533,-1873,2302,-2797,3407

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

%C Limiting ratio a(n+1)/a(n) is -1.2207440846057594..., which is a root of z^4 + z - 1.

%H Robert Israel, <a href="/A177825/b177825.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,2,-1).

%F Recurrence a(i)= a(i-1) - a(i-3) + 2 a(i-4) - a(i-5).

%F a(n) = (-1)^n*A175790(n).

%p N:= 100: # to get terms up to index N

%p for i from 0 to 4 do a[i]:= coeftayl(1/(1+x^3-x^4)/(1-x),x=0,i) end do:

%p for i from 5 to N do a[i]:= a[i-1] - a[i-3] + 2*a[i-4] - a[i-5] end do:

%p [seq(a[i],i=0..N)]; # _Robert Israel_, Feb 11 2013

%t CoefficientList[ Series[1/(1 - x + x^3 - 2 x^4 + x^5), {x, 0, 50}], x] (* Or *)

%t LinearRecurrence[{1, 0, -1, 2, -1}, {1, 1, 1, 0, 1}, 51] (* _Robert G. Wilson v_, Feb 11 2013 *)

%Y Cf. A175790.

%K sign,easy

%O 0,7

%A _Roger L. Bagula_, Dec 13 2010

%E Recurrence, reference to A175790, and comment edited by _Robert Israel_, Feb 11 2013

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)