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%I #23 Apr 19 2023 02:33:05
%S 0,0,0,1,4,8,33,68,245,549,1815,4331,13524,33766,101383,261293,763745,
%T 2011959,5774140,15440569,43764595,118231475,332290914,903952326,
%U 2526016085,6904206021,19218113777,52696460176,146294791786,402018135352,1114070627578
%N Expansion of g.f.: x^3*(1 + 4*x - x^2 - 6*x^3 + x^4)/(1 - 9*x^2 - 3*x^3 + 17*x^4 + 8*x^5 - 6*x^6 - 7*x^7 + x^8 - x^9).
%H G. C. Greubel, <a href="/A173652/b173652.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,9,3,-17,-8,6,7,-1,1).
%t M = {{0, 1, 0, 1, 0, 0, 0, 0, 0},
%t {0, 0, 1, 0, 1, 0, 0, 0, 0},
%t {1, 1, 0, 0, 0, 1, 0, 0, 0},
%t {1, 0, 0, 0, 0, 1, 1, 0, 0},
%t {0, 1, 0, 1, 0, 1, 0, 1, 0},
%t {0, 0, 1, 0, 1, 0, 0, 0, 1},
%t {0, 0, 0, 1, 0, 0, 0, 1, 0},
%t {0, 0, 0, 0, 1, 0, 0, 0, 1},
%t {0, 0, 0, 0, 0, 1, 1, 1, 0}};
%t v[0]= {0, 0, 0, 0, 0, 0, 0, 0, 1};
%t v[n_] := v[n] = M.v[n - 1]
%t Table[v[n][[1]], {n, 0, 30}] (* or *)
%t LinearRecurrence[{0, 9, 3, -17, -8, 6, 7, -1, 1}, {0, 0, 0, 1, 4, 8, 33, 68, 245}, 31] (* _Georg Fischer_, May 03 2019 *)
%t CoefficientList[Series[x^3*(1+4*x-x^2-6*x^3+x^4)/(1-9*x^2-3*x^3+17*x^4 + 8*x^5-6*x^6-7*x^7+x^8-x^9), {x,0,30}], x] (* _G. C. Greubel_, May 03 2019 *)
%o (PARI) my(x='x+O('x^30)); concat([0,0,0], Vec(x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5-6*x^6-7*x^7+x^8-x^9))) \\ _G. C. Greubel_, May 03 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0,0,0] cat Coefficients(R!( x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5 -6*x^6-7*x^7+x^8-x^9) )); // _G. C. Greubel_, May 03 2019
%o (Sage) (x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3 +17*x^4+8*x^5-6*x^6 -7*x^7+x^8-x^9)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 03 2019
%Y Cf. A000931.
%K nonn,easy,less
%O 0,5
%A _Roger L. Bagula_, Nov 24 2010
%E Definition corrected by _Georg Fischer_, May 03 2019
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