A016307 Expansion of 1/((1-2*x)*(1-6*x)*(1-10*x)).

1, 18, 232, 2640, 28336, 295008, 3020032, 30620160, 308720896, 3102325248, 31113951232, 311683706880, 3120102240256, 31220613439488, 312323680632832, 3123942083788800, 31243652502716416, 312461915016265728

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-92,120).

Formula

G.f.: 1/((1-2*x)*(1-6*x)*(1-10*x)).

From Vincenzo Librandi, Sep 01 2011: (Start)

a(n) = (2^n - 18*6^n + 25*10^n)/8.

a(n) = 18*a(n-1) - 92*a(n-2) + 120*a(n-3) for n > 2.

a(n) = 16*a(n-1) - 60*a(n-2) + 2^n for n > 1. (End)

Mathematica

CoefficientList[Series[1/((1-2x)(1-6x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -92, 120}, {1, 18, 232}, 30] (* Harvey P. Dale, Nov 06 2019 *)

Prog

(Magma) [(2^n-18*6^n+25*10^n)/8: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

Crossrefs

Sequence in context: A296941 A016312 A017916 * A193982 A021094 A275963

Adjacent sequences: A016304 A016305 A016306 * A016308 A016309 A016310

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved