A016311 Expansion of 1/((1-2*x)*(1-7*x)*(1-8*x)).

1, 17, 203, 2101, 20163, 184821, 1643251, 14298917, 122461955, 1036190485, 8684988819, 72248167173, 597363137827, 4914549713909, 40265910006707, 328773866154469, 2676717032006979, 21739418975585493

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (17,-86,112).

Crossrefs

Cf. A016130, A016131. - Zerinvary Lajos, Jun 05 2009

Programs

Magma

[(160*8^n-147*7^n+2*2^n)/15: n in [0..20]]; // Vincenzo Librandi, Sep 02 2011

Mathematica

CoefficientList[Series[1/((1-2x)(1-7x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{17,-86,112},{1,17,203},30] (* Harvey P. Dale, Jul 12 2012 *)

Sage

[(8^n - 2^n)/6-(7^n - 2^n)/5 for n in range(2,21)] # Zerinvary Lajos, Jun 05 2009

Formula

a(n) = A016131(n+1) - A016130(n+1). - Zerinvary Lajos, Jun 05 2009

a(n) = 4*8^(n+1)/3 - 7^(n+2)/5 + 2^(n+1)/15. - R. J. Mathar, Mar 14 2011

From Vincenzo Librandi, Sep 02 2011: (Start)

a(n) = (160*8^n - 147*7^n + 2*2^n)/15;

a(n) = 15*a(n-1) - 56*a(n-2) + 2^n. (End)

a(n) = 17*a(n-1) - 86*a(n-2) + 112*a(n-3), with a(0)=1, a(1)=17, a(2)=203. - Harvey P. Dale, Jul 12 2012