A016234 - OEIS

%I #26 Sep 04 2017 03:42:03

%S 1,15,166,1650,15631,144585,1320796,11984820,108351661,977606355,

%T 8810664226,79357013190,714518294491,6432190529325,57897344158456,

%U 521114244398760,4690218934452121,42212924084385495

%N Expansion of 1/((1-x)(1-5x)(1-9x)).

%H Harvey P. Dale, <a href="/A016234/b016234.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15, -59, 45).

%F a(0)=1, a(1)=15, a(n) = 14*a(n-1) - 45*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011

%F a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32. - _Yahia Kahloune_, Aug 13 2013

%F a(0)=1, a(1)=15, a(2)=166, a(n) = 15*a(n-1) - 59*a(n-2) + 45*a(n-3). - _Harvey P. Dale_, Oct 16 2014

%F O.g.f.: see the name.

%F E.g.f.: (d^2/dx^2) (exp(x)*((exp(4*x) - 1)^2)/(4^2*2!)) = exp(x)*(1 - 50*exp(4*x) + 81*exp(8*x))/32.

%t CoefficientList[Series[1/((1-x)(1-5x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-59,45},{1,15,166},30] (* _Harvey P. Dale_, Oct 16 2014 *)

%o (PARI) Vec(1/((1-x)*(1-5*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (PARI) a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32; \\ _Joerg Arndt_, Aug 13 2013

%Y Cf. A000012, A003463.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_