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%I #36 Mar 09 2024 14:50:43
%S -1,1,7,9,-17,-79,-73,249,863,481,-3353,-9111,-1457,42641,92567,
%T -28071,-518977,-897599,799687,6087369,8176303,-14084239,-69049993,
%U -67678791,209892383,758178721,466895527,-2857102551,-8048682737,-1811852719
%N Expansion of (-1+3*x)/(5*x^2 + 1 - 2*x).
%C Binomial transform of signed powers of 2: (-1, 2, 4, -8, -16, 32, 64, -128, -256, 512, 1024). Inverse binomial transform of (-1, 0, 8, 32, 64, 0, -512, -2048, -4096, 0, 32768, 131072, 262144, 0, -2097152, -8388608). Compare with A116483.
%C Floretion Algebra Multiplication Program, FAMP Code: 2basekforseq[A*B] with A = - .5'i + .5'j - .5i' + .5j' + 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj' and B = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' ; 1vesforseq = A000004
%H Harvey P. Dale, <a href="/A116484/b116484.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Riordan, <a href="http://www.jstor.org/stable/2005477">The distribution of crossings of chords joining pairs of 2n points on a circle</a>, Math. Comp., 29 (1975), 215-222.
%H J. Riordan, <a href="/A003480/a003480.pdf">The distribution of crossings of chords joining pairs of 2n points on a circle</a>, Math. Comp., 29 (1975), 215-222. [Annotated scanned copy]
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-5).
%F a(n) = 3*A045873(n) - A045873(n+1). - _R. J. Mathar_, Apr 23 2009
%F E.g.f.: exp(x)*(sin(2*x) - cos(2*x)). - _Arkadiusz Wesolowski_, Aug 31 2012
%F a(0)=-1, a(1)=1, a(n) = 2*a(n-1) - 5*a(n-2). - _Harvey P. Dale_, Jun 24 2013
%F a(n) = (1/2)*((-1 - i)*(1 + 2*i)^n - (1 - i)*(1 - 2*i)^n), n >= 0, where i=sqrt(-1). - _Taras Goy_, Apr 20 2019
%t CoefficientList[Series[(-1+3x)/(5x^2+1-2x),{x,0,40}],x] (* or *) LinearRecurrence[{2,-5},{-1,1},40] (* _Harvey P. Dale_, Jun 24 2013 *)
%Y Cf. A000079, A006495, A116483.
%K easy,sign
%O 0,3
%A _Creighton Dement_, Feb 17 2006
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