A016311 - OEIS

%I #26 Sep 08 2022 08:44:41

%S 1,17,203,2101,20163,184821,1643251,14298917,122461955,1036190485,

%T 8684988819,72248167173,597363137827,4914549713909,40265910006707,

%U 328773866154469,2676717032006979,21739418975585493

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

%H Vincenzo Librandi, <a href="/A016311/b016311.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-86,112).

%F a(n) = A016131(n+1) - A016130(n+1). - _Zerinvary Lajos_, Jun 05 2009

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

%F From _Vincenzo Librandi_, Sep 02 2011: (Start)

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

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

%F 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

%t 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 *)

%o (Sage) [(8^n - 2^n)/6-(7^n - 2^n)/5 for n in range(2,21)] # _Zerinvary Lajos_, Jun 05 2009

%o (Magma) [(160*8^n-147*7^n+2*2^n)/15: n in [0..20]]; // _Vincenzo Librandi_, Sep 02 2011

%Y Cf. A016130, A016131. - _Zerinvary Lajos_, Jun 05 2009

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_