A016317 Expansion of 1/((1-2x)(1-8x)(1-10x)).

1, 20, 284, 3520, 40656, 450240, 4851904, 51315200, 535521536, 5534172160, 56773377024, 579187015680, 5883496124416, 59567968993280, 601543751942144, 6062350015528960, 60998800124215296, 612990400993689600

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (20,-116, 160).

Formula

From Vincenzo Librandi, Oct 09 2011: (Start)

a(n) = (75*10^n + 2^n - 8^(n+2))/12.

a(n) = 18*a(n-1) - 80*a(n-2) + 2^n.

a(n) = 20*a(n-1) - 116*a(n-2) + 160*a(n-3), n >= 3. (End)

Mathematica

CoefficientList[Series[1/((1 - 2 x) (1 - 8 x) (1 - 10 x)), {x, 0, 17}], x] (* Michael De Vlieger, Jan 31 2018 *)
LinearRecurrence[{20, -116, 160}, {1, 20, 284}, 20] (* Harvey P. Dale, Mar 20 2020 *)

Prog

(Sage) [((10^n - 2^n)/8-(8^n - 2^n)/6)/2 for n in range(2, 20)] # Zerinvary Lajos, Jun 05 2009
(Magma) [((75*10^n + 2^n -8^(n+2))/12) : n in [0..20]]; // Vincenzo Librandi, Oct 09 2011
(PARI) Vec(1/((1-2*x)*(1-8*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A019040 A021204 A017953 * A021404 A046175 A231105

Adjacent sequences: A016314 A016315 A016316 * A016318 A016319 A016320

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved