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 #20 Aug 12 2023 17:12:13
%S 1,18,229,2562,27061,278058,2818549,28377522,284741941,2852272698,
%T 28547052469,285592329282,2856532847221,28568377838538,
%U 285699029999989,2857066572421842,28571047129374901,285712378448671578
%N Expansion of 1/((1-3x)(1-5x)(1-10x)).
%H Vincenzo Librandi, <a href="/A017916/b017916.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (18,-95,150).
%F a(0)=1, a(2)=18, a(3)=229, a(n) = 18*a(n-1)-95*a(n-2)+150*a(n-3). - _Vincenzo Librandi_, Jul 01 2013
%F a(n) = 15*a(n-1) -50*a(n-2) -3^n. - _Vincenzo Librandi_, Jul 01 2013
%F a(n) = (2*10^(n+2) - 7*5^(n+2) + 5*3^(n+2))/70. [_Yahia Kahloune_, Aug 13 2013]
%p a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [18, -95, 150][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 01 2013
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 10 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t LinearRecurrence[{18,-95,150},{1,18,229},20] (* _Harvey P. Dale_, Aug 12 2023 *)
%o (Magma) I:=[1, 18, 229]; [n le 3 select I[n] else 18*Self(n-1)-95*Self(n-2)+150*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 01 2013
%o (PARI) a(n) = (2*10^(n+2) - 7*5^(n+2) + 5*3^(n+2))/70; \\ _Joerg Arndt_, Aug 13 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.