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%I #16 Feb 10 2024 13:50:32
%S 1,-1,4,-9,24,-60,154,-391,997,-2538,6465,-16464,41932,-106792,271981,
%T -692685,1764144,-4492953,11442736,-29142568,74220826,-189026955,
%U 481417305,-1226082390,3122609041,-7952717776,20254126984,-51583580784,131374006329,-334585720425,852129027964
%N Expansion of (1-x)^(-1)/(1+2*x-x^2+x^3).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3,-2,1)
%F a(n) = (1 + 2*A077986(n) + A077986(n-2))/3. - _R. J. Mathar_
%p A077986 := proc(n) if n < 0 then 0; else coeftayl( 1/(1+2*x-x^2+x^3),x=0,n) ; end if; end proc:
%p A077922 := proc(n) (1+2*A077986(n)+A077986(n-2))/3 ; end proc:
%p seq(A077922(n),n=0..20) ; # _R. J. Mathar_, Mar 24 2011
%t CoefficientList[Series[1/((1 + 2*x - x^2 + x^3)(1 - x)), {x, 0, 30}], x]
%t LinearRecurrence[{-1,3,-2,1},{1,-1,4,-9},40] (* _Harvey P. Dale_, Feb 10 2024 *)
%o (PARI) Vec((1-x)^(-1)/(1+2*x-x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A010907.
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
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