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A137247 a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 3*a(n-4), with initial terms 0, 0, 0, 1.

%I A137247 #25 Jan 02 2024 08:58:54
%S A137247 0,0,0,1,4,10,22,49,112,256,580,1309,2956,6682,15106,34141,77152,
%T A137247 174352,394024,890473,2012404,4547866,10277806,23227033,52491280,
%U A137247 118626160,268085740,605852581,1369179004,3094236490,6992730202,15803018149
%N A137247 a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 3*a(n-4), with initial terms 0, 0, 0, 1.
%C A137247 Essentially the partial sums of A052103. - _R. J. Mathar_, Apr 01 2008
%H A137247 G. C. Greubel, <a href="/A137247/b137247.txt">Table of n, a(n) for n = 0..1000</a>
%H A137247 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,6,-3).
%F A137247 From _R. J. Mathar_, Apr 01 2008: (Start)
%F A137247 O.g.f.: x^3/((1-x)*(1-3*x+3*x^2-3*x^3)).
%F A137247 A052103(n) = a(n+2) - a(n+1). (End)
%p A137247 a[0]:=0: a[1]:=0: a[2]:=0: a[3]:=1: for n from 4 to 30 do a[n]:=4*a[n-1]-6*a[n-2]+6*a[n-3]-3*a[n-4] end do: seq(a[n],n=0..30); # _Emeric Deutsch_, Mar 17 2008
%t A137247 LinearRecurrence[{4,-6,6,-3}, {0,0,0,1}, 41] (* _G. C. Greubel_, Apr 15 2021 *)
%o A137247 (Magma) I:=[0,0,0,1]; [n le 4 select I[n] else 4*Self(n-1) -6*Self(n-2) +6*Self(n-3) -3*Self(n-4): n in [1..41]]; // _G. C. Greubel_, Apr 15 2021
%o A137247 (Sage)
%o A137247 def A137247_list(prec):
%o A137247     P.<x> = PowerSeriesRing(ZZ, prec)
%o A137247     return P( x^3/((1-x)*(1-3*x+3*x^2-3*x^3)) ).list()
%o A137247 A137247_list(40) # _G. C. Greubel_, Apr 15 2021
%Y A137247 Cf. A052103.
%K A137247 nonn,easy
%O A137247 0,5
%A A137247 _Paul Curtz_, Mar 10 2008
%E A137247 More terms from _R. J. Mathar_, _Rolf Pleisch_ and _Emeric Deutsch_, Apr 01 2008
%E A137247 Name edited by _Michel Marcus_, Jan 29 2019