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Expansion of 1/((1-5*x)*(1-9*x)).
4

%I #22 Nov 09 2024 04:14:57

%S 1,14,151,1484,13981,128954,1176211,10664024,96366841,869254694,

%T 7833057871,70546348964,635161281301,5717672234834,51465153629131,

%U 463216900240304,4169104690053361,37522705149933374,337708161046665991

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

%H G. C. Greubel, <a href="/A016163/b016163.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-45).

%F a(n) = ((7+sqrt4)^n - (7-sqrt4)^n)/4. Offset 1. a(3)=151. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008

%F a(n) = 14*a(n-1) - 45*a(n-2). - _Philippe Deléham_, Jan 01 2009

%F a(0)=1, a(n) = 9*a(n-1) + 5^n. - _Vincenzo Librandi_, Feb 09 2011

%F From _G. C. Greubel_, Nov 09 2024: (Start)

%F a(n) = (9^(n+1) - 5^(n+1))/4.

%F E.g.f.: (1/4)*(9*exp(9*x) - 5*exp(5*x)). (End)

%t Table[(9^(n+1) - 5^(n+1))/4, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)

%o (Magma) [(9^(n+1) - 5^(n+1))/4: n in [0..30]]; // _G. C. Greubel_, Nov 09 2024

%o (SageMath)

%o def A016163(n): return (9^(n+1) - 5^(n+1))/4

%o [A016163(n) for n in range(31)] # _G. C. Greubel_, Nov 09 2024

%Y Cf. A016142, A016161.

%K nonn

%O 0,2

%A _N. J. A. Sloane_