A018206 Expansion of 1/((1-3x)(1-10x)(1-11x)).

1, 24, 403, 5850, 78601, 1007364, 12509263, 151886670, 1813607701, 21378247704, 249446413723, 2886767617890, 33183014997601, 379298878576044, 4315144805143783, 48895164279003510, 552132521336304301

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 (24,-173,330).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-10*x)*(1-11*x)))); // Vincenzo Librandi, Jul 02 2013

Magma

I:=[1, 24, 403]; [n le 3 select I[n] else 24*Self(n-1)-173*Self(n-2)+330*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{24,-173,330},{1,24,403},20] (* Harvey P. Dale, Nov 25 2013 *)

Formula

a(0)=1, a(1)=24, a(2)=403; for n>2, a(n) = 24*a(n-1) -173*a(n-2) +330*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 21*a(n-1) -110*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (7*11^(n+2) - 8*10^(n+2) + 3^(n+2))/56. [Yahia Kahloune, Jul 06 2013]