A016306 Expansion of 1/((1-2*x)*(1-6*x)*(1-9*x)).

1, 17, 205, 2165, 21421, 204437, 1909885, 17608805, 160998541, 1464103157, 13267627165, 119952839045, 1082840722861, 9765157542677, 88003964122045, 792740954558885, 7138900255858381, 64275492291826997

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (17,-84,108).

Formula

G.f.: 1/((1-2*x)*(1-6*x)*(1-9*x)).

From Vincenzo Librandi, Sep 01 2011: (Start)

a(n) = (2^n - 21*6^n + 27*9^n)/7.

a(n) = 17*a(n-1) - 84*a(n-2) + 108*a(n-3) for n > 2.

a(n) = 15*a(n-1) - 54*a(n-2) + 2^n. (End)

Mathematica

CoefficientList[Series[1/((1-2x)(1-6x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{17, -84, 108}, {1, 17, 205}, 30] (* Harvey P. Dale, Jan 19 2019 *)

Prog

(Magma) [(2^n-21*6^n+27*9^n)/7: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

Crossrefs

Sequence in context: A017897 A016311 A140961 * A021092 A219124 A246989

Adjacent sequences: A016303 A016304 A016305 * A016307 A016308 A016309

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved