|
%I #20 Sep 08 2022 08:44:45
%S 1,30,607,10344,160189,2335746,32694859,444486828,5913240457,
%T 77372622822,999305059831,12772807490352,161880145667605,
%U 2037329650638858,25491080959642723,317372095748963316,3934768748483886433,48606797206780217454,598568489369669902735
%N Expansion of 1/((1-7*x)*(1-11*x)*(1-12*x)).
%H G. C. Greubel, <a href="/A020975/b020975.txt">Table of n, a(n) for n = 0..920</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (30,-293,924).
%F a(n) = 30*a(n-1) - 293*a(n-2) + 924*a(n-3), n>=3. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 23*a(n-1) - 132*a(n-2) + 7^n, a(0)=1, a(1)=30. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 49*7^n/20 - 121*11^n/4 + 144*12^n/5. - _R. J. Mathar_, Jul 01 2013
%p seq(coeftayl(1/((1-7*x)*(1-11*x)*(1-12*x)), x = 0, k), k=0..17); # _Muniru A Asiru_, Feb 10 2018
%t CoefficientList[Series[1/((1-7*x)*(1-11*x)*(1-12*x)), {x,0,50}], x] (* _G. C. Greubel_, Feb 09 2018 *)
%t LinearRecurrence[{30, -293, 924}, {1, 30, 607}, 20] (* _Robert G. Wilson v_, Feb 10 2018 *)
%o (PARI) x='x+O('x^30); Vec(1/((1-7*x)*(1-11*x)*(1-12*x))) \\ _G. C. Greubel_, Feb 09 2018
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!(1/((1-7*x)*(1-11*x)*(1-12*x)))); // _G. C. Greubel_, Feb 09 2018
%o (GAP) a:=[1,30,607];; for n in [4..17] do a[n]:=30*a[n-1]-293*a[n-2]+924*a[n-3]; od; a; # _Muniru A Asiru_, Feb 10 2018
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E a(16)-a(17) from _Muniru A Asiru_, Feb 10 2018
|
