cp's OEIS Frontend

A156096 Inverse binomial transform of A030186.

%I A156096 #13 Sep 08 2022 08:45:41
%S A156096 1,1,4,6,18,32,84,164,400,824,1928,4096,9360,20240,45632,99680,223008,
%T A156096 489984,1091392,2405952,5345536,11806592,26194048,57917440,128389376,
%U A156096 284057856,629392384,1393010176,3085685248,6830825472,15128761344
%N A156096 Inverse binomial transform of A030186.
%C A156096 A030186 = (1, 2, 7, 22, 71, 228, 733, 2356, 7573, 24342, ...).
%H A156096 G. C. Greubel, <a href="/A156096/b156096.txt">Table of n, a(n) for n = 0..1000</a>
%H A156096 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,2).
%F A156096 a(n) = A007318^(-1) * A030186
%F A156096 From _R. J. Mathar_, Feb 10 2009: (Start)
%F A156096 a(n) = 4*a(n-2) + 2*a(n-3).
%F A156096 G.f.: (1+x)/(1-4*x^2-2*x^3). (End)
%e A156096 a(3) = 6 = (-1, 3, -3, 1) dot (1, 2, 7, 22) = (-1, 6, -21, 22) = 6.
%p A156096 seq(coeff(series((1+x)/(1-4*x^2-2*x^3), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Oct 27 2019
%t A156096 LinearRecurrence[{0,4,2},{1,1,4},40] (* _Harvey P. Dale_, Apr 05 2014 *)
%o A156096 (PARI) my(x='x+O('x^40)); Vec((1+x)/(1-4*x^2-2*x^3)) \\ _G. C. Greubel_, Oct 27 2019
%o A156096 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-4*x^2-2*x^3) )); // _G. C. Greubel_, Oct 27 2019
%o A156096 (Sage)
%o A156096 def A156096_list(prec):
%o A156096     P.<x> = PowerSeriesRing(ZZ, prec)
%o A156096     return P((1+x)/(1-4*x^2-2*x^3)).list()
%o A156096 A156096_list(40) # _G. C. Greubel_, Oct 27 2019
%o A156096 (GAP) a:=[1,1,4];; for n in [4..40] do a[n]:=4*a[n-2]+2*a[n-3]; od; a; # _G. C. Greubel_, Oct 27 2019
%Y A156096 Cf. A030186.
%K A156096 nonn
%O A156096 0,3
%A A156096 _Gary W. Adamson_, Feb 03 2009
%E A156096 More terms from _R. J. Mathar_, Feb 10 2009