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%I #15 Sep 08 2022 08:45:38
%S 0,1,1,2,4,9,18,36,72,145,291,583,1167,2336,4675,9354,18713,37433,
%T 74876,149766,299551,599128,1198292,2396634,4793337,9586769,19173669,
%U 38347519,76695288,153390921,306782318,613565293,1227131493,2454264238
%N Antidiagonal sums of A145153.
%H Vincenzo Librandi, <a href="/A145139/b145139.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,1,-2).
%F G.f.: x*(1-x)^2 / ((1-2*x)*(1-x-x^4)).
%p a:= n-> (Matrix([[4, 2, 1, 1, 0]]). Matrix (5, (i,j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0, 1, -2][i] else 0 fi)^n)[1,5]: seq(a(n), n=0..40);
%t CoefficientList[Series[x*(1-x)^2/((1-2*x)*(1-x-x^4)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%o (PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1-x)^2/((1-2*x)*(1-x-x^4)))) \\ _G. C. Greubel_, May 21 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x*(1-x)^2/((1-2*x)*(1-x-x^4)) )); // _G. C. Greubel_, May 21 2019
%o (Sage) (x*(1-x)^2/((1-2*x)*(1-x-x^4))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, May 21 2019
%o (GAP) a:=[0,1,1,2,4];; for n in [6..40] do a[n]:=3*a[n-1]-2*a[n-2]+a[n-4] -2*a[n-5]; od; a; # _G. C. Greubel_, May 21 2019
%Y Cf. A145153, A000004, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130, A017898, A003269, A098578, A145131, A145132, A145133, A145134, A145135, A145136, A145137.
%K nonn,easy
%O 0,4
%A _Alois P. Heinz_, Oct 03 2008
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