A019839 Expansion of 1/((1-5x)(1-6x)(1-10x)).

1, 21, 301, 3681, 41461, 445641, 4658221, 47871201, 486836581, 4919066361, 49504632541, 496978967121, 4981629662101, 49888557269481, 499325240101261, 4995920923029441, 49975372950286021, 499851474762263001, 4999105033876312381, 49994611129771546161

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (21,-140,300).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 21, 301]; [n le 3 select I[n] else 21*Self(n-1)-140*Self(n-2)+300*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [21, -140, 300][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Formula

G.f.: 1/((1-5*x)*(1-6*x)*(1-10*x)).

a(n) = 5*5^n - 9*6^n + 5*10^n. - R. J. Mathar, Jun 29 2013

a(n) = 21*a(n-1) - 140*a(n-2) + 300*a(n-3), with a(0)=1, a(1)=21, a(2)=301. - Vincenzo Librandi, Jul 03 2013

a(n) = 16*a(n-1) - 60*a(n-2) + 5^n. - Vincenzo Librandi, Jul 03 2013