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Expansion of 1/((1-5x)(1-6x)(1-8x)).
1

%I #19 Nov 30 2024 16:13:04

%S 1,19,243,2615,25571,235599,2086603,17981815,151979091,1266533279,

%T 10446235163,85502523015,695860175011,5639142048559,45552803794923,

%U 367090952376215,2952891339001331,23720875971413439

%N Expansion of 1/((1-5x)(1-6x)(1-8x)).

%H Vincenzo Librandi, <a href="/A019783/b019783.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-118,240).

%F From _Vincenzo Librandi_, Oct 09 2011: (Start)

%F a(n) = (8^(n+2) + 2*5^(n+2) - 3*6^(n+2))/6.

%F a(n) = 14*a(n-1) - 48*a(n-2) + 5^n.

%F a(n) = 19*a(n-1) - 118*a(n-2) + 240*a(n-3), n >= 3. (End)

%t CoefficientList[Series[1/((1-5x)(1-6x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{19,-118,240},{1,19,243},30] (* _Harvey P. Dale_, Nov 30 2024 *)

%o (Magma) [(8^(n+2)+2*5^(n+2)-3*6^(n+2))/6 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011

%o (PARI) Vec(1/((1-5*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_