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a(n) = (5*6^n+(-6)^n)/6.
3

%I #17 Sep 08 2022 08:45:10

%S 1,4,36,144,1296,5184,46656,186624,1679616,6718464,60466176,241864704,

%T 2176782336,8707129344,78364164096,313456656384,2821109907456,

%U 11284439629824,101559956668416,406239826673664,3656158440062976

%N a(n) = (5*6^n+(-6)^n)/6.

%H Vincenzo Librandi, <a href="/A083223/b083223.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,36).

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

%F G.f.: (1+4*x)/((1+6*x)*(1-6*x)).

%F E.g.f.: (5*exp(6*x)+exp(-6*x))/6.

%F a(n) = 36*a(n-2). - _Wesley Ivan Hurt_, Jun 24 2021

%t CoefficientList[Series[(1+4x)/((1+6x)(1-6x)),{x,0,50}],x] (* _Harvey P. Dale_, Mar 01 2011 *)

%o (Magma) [(5*6^n+(-6)^n)/6: n in [0..25]]; // _Vincenzo Librandi_, Jun 29 2011

%Y Cf. A083222, A083224.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 23 2003