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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (24,-173,330).

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]

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 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-10*x)*(1-11*x)))); /* or */ 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

Crossrefs

Sequence in context: A021674 A019677 A021314 * A021304 A018092 A331931

Adjacent sequences: A018203 A018204 A018205 * A018207 A018208 A018209

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved