A016305 Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)).

1, 16, 180, 1760, 16016, 139776, 1188160, 9925120, 81920256, 670478336, 5454525440, 44180398080, 356708356096, 2873257885696, 23103609323520, 185534152048640, 1488504881217536, 11933429038841856, 95619772245606400

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-76,96).

Formula

G.f.: 1/((1-2*x)*(1-6*x)*(1-8*x)).

a(n) = 2^(n-1)*(2^(2*n+5) - 3^(n+3) + 1)/3. - Zerinvary Lajos, Jun 05 2009

From Vincenzo Librandi, Sep 01 2011: (Start)

a(n) = 16*a(n-1) - 76*a(n-2) + 96*a(n-3) for n > 2;

a(n) = 14*a(n-1) - 48*a(n-2) + 2^n for n > 1. (End)

Mathematica

CoefficientList[Series[1/((1-2x)(1-6x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -76, 96}, {1, 16, 180}, 30] (* Harvey P. Dale, Feb 21 2015 *)

Prog

(Sage) [((8^n - 2^n)/6-(6^n - 2^n)/4)/2 for n in range(2, 21)] # Zerinvary Lajos, Jun 05 2009
(Magma) [2^(n-1)*(2^(2*n+5)-3^(n+3)+1)/3: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

Crossrefs

Sequence in context: A227557 A269202 A269103 * A218895 A016909 A001455

Adjacent sequences: A016302 A016303 A016304 * A016306 A016307 A016308

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved