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%I #10 Jan 07 2019 04:39:54
%S 0,1,1,-7,-15,33,145,-71,-1119,-767,7137,13625,-35567,-138079,97265,
%T 1099385,556609,-7236351,-12231999,37865849,130726193,-122102751,
%U -1075051951,-351058887,7296407521,10828871681,-39894922079,-122993431367,145442151505,1046291093153
%N Expansion of x*(1 - x^2)/(1 - x + 7*x^2 + x^3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-7,-1).
%F G.f.: (1/2)*(x/(1 - x))*g(f(x)), where f(x) = (1 + x)/(-1 + x), and g(x) = (1-x^2)/(1 - x^2 - x^3) is the g.f. of the Padovan sequence A000931.
%F a(n) = a(n-1) - 7*a(n-2) - a(n-3), n >= 4. - _Franck Maminirina Ramaharo_, Jan 06 2019
%t CoefficientList[Series[x*(1 - x^2)/(1 - x + 7*x^2 + x^3), {x, 0, 50}], x]
%o (Maxima) (a[0] : 0, a[1] : 1, a[2] : 1, a[3] : -7, a[n] := a[n-1] - 7*a[n-2] - a[n-3], makelist(a[n], n, 0, 50)); /* _Franck Maminirina Ramaharo_, Jan 06 2019 */
%Y Cf. A000931
%K sign,easy,less
%O 0,4
%A _Roger L. Bagula_, Mar 29 2010
%E Edited by _Franck Maminirina Ramaharo_, Jan 06 2019
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