Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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