A024346 - OEIS

%I #37 Jan 21 2025 18:20:28

%S 1,27,484,7266,98959,1269177,15642586,187539120,2204181925,

%T 25529358855,292445725936,3321943348542,37489352241979,

%U 420930326166741,4707254688375814,52473555698990412,583456285162491601

%N Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)).

%H Vincenzo Librandi, <a href="/A024346/b024346.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (27,-245,813,-594).

%F a(n) = 27*a(n-1) - 245*a(n-2) + 813*a(n-3) - 594*a(n-4) for n > 3; a(0)=1, a(1)=27, a(2)=484, a(3)=7266. - _Vincenzo Librandi_, Jul 16 2013

%F a(n) = (12*11^(n+3) - 25*9^(n+3) + 16*6^(n+3) - 3)/1200. - _Yahia Kahloune_, Aug 13 2013

%F E.g.f.: (1/400)*(-exp(x) + 1152*exp(6*x) - 6075*exp(9*x) + 5324*exp(11*x)). - _G. C. Greubel_, Jan 30 2022

%t CoefficientList[Series[1/((1-x)(1-6x)(1-9x)(1-11x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)

%t LinearRecurrence[{27,-245,813,-594},{1,27,484,7266},20] (* _Harvey P. Dale_, Oct 13 2016 *)

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 16 2013

%o (Magma) I:=[1,27,484,7266]; [n le 4 select I[n] else 27*Self(n-1)-245*Self(n-2)+813*Self(n-3)-594*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 16 2013

%o (PARI) a(n) = (12*11^(n+3) - 25*9^(n+3) + 16*6^(n+3) - 3)/1200; \\ _Joerg Arndt_, Aug 13 2013

%o (Sage) [(4*11^(n+3) -75*9^(n+2) +32*6^(n+2) -1)/400 for n in (0..20)] # _G. C. Greubel_, Jan 30 2022

%Y Cf. A003464, A016244, A024347.

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_