A018091 Expansion of 1/((1-3*x)*(1-9*x)*(1-11*x)).

1, 23, 370, 5150, 66451, 819413, 9810340, 115087100, 1330524901, 15216894803, 172615989910, 1945847389850, 21827965327351, 243920416546193, 2717439768299080, 30200674142257400, 334986945826585801, 3709872176577373583, 41033735895102897850, 453397372422060233750

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 (23,-159,297).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-9*x)*(1-11*x)))); // Vincenzo Librandi, Jul 02 2013

Magma

I:=[1, 23, 370]; [n le 3 select I[n] else 23*Self(n-1)-159*Self(n-2)+297*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)

Formula

a(0)=1, a(1)=23, a(2)=370; for n>2, a(n) = 23*a(n-1) -159*a(n-2) +297*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 20*a(n-1) -99*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (3*11^(n+2) - 4*9^(n+2) + 3^(n+2))/48. - Yahia Kahloune, Jul 06 2013