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%I #17 Mar 14 2024 15:19:46
%S 1,-3,-5,7,26,0,-97,-97,265,627,-362,-2702,-1351,8733,13775,-18817,
%T -70226,0,262087,262087,-716035,-1694157,978122,7300802,3650401,
%U -23596563,-37220045,50843527,189750626,0,-708158977,-708158977,1934726305,4577611587,-2642885282,-19726764302,-9863382151
%N Expansion of (1-x)*(2*x^2-4*x+1)/(1-2*x+5*x^2-4*x^3+x^4).
%C Unsigned bisection gives match to A002316 (Related to Bernoulli numbers). Note that all numbers in A002316 appear to be in A002531 (Numerators of continued fraction convergents to sqrt(3)) as well. a(12*n+5) = (0,0,0,0,...)
%C Floretion Algebra Multiplication Program, FAMP Code: 2tesseq['i + .5i' + .5j' + .5k' + .5e]
%H Robert Israel, <a href="/A131039/b131039.txt">Table of n, a(n) for n = 0..3492</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-5,4,-1).
%F a(0)=1, a(1)=-3, a(2)=-5, a(3)=7, a(n)=2*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4) [_Harvey P. Dale_, Aug 31 2011]
%p f:= gfun:-rectoproc({a(0)=1, a(1)=-3, a(2)=-5, a(3)=7, a(n)=2*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4)},a(n),remember):
%p map(f, [$0..100]); # _Robert Israel_, Dec 25 2016
%t CoefficientList[Series[(1-x)(2x^2-4x+1)/(1-2x+5x^2-4x^3+x^4),{x, 0, 50}], x] (* or *) LinearRecurrence[{2,-5,4,-1},{1,-3,-5,7},50] (* _Harvey P. Dale_, Aug 31 2011 *)
%Y Cf. A131040, A131041, A131042, A002316, A002531.
%K easy,sign
%O 0,2
%A _Creighton Dement_, Jun 11 2007
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