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%I #44 Sep 08 2022 08:46:19
%S 1,2,14,38,206,662,3134,11078,48686,181622,765854,2945318,12135566,
%T 47479382,193106174,762858758,3080132846,12234437942,49196032094,
%U 196009287398,786361672526,3138473121302,12574813191614,50236490647238,201134248946606,803972136713462,3217583124072734
%N a(n) = a(n-1) + 12*a(n-2) with a(1) = 1 and a(2) = 2.
%C The binomial transform is 1, 3, 19, 87,.... (A015528 shifted). - _R. J. Mathar_, Apr 07 2022
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,12).
%F a(n) = (5/28)*4^n - (2/21)*(-3)^n.
%F G.f.: x*(1+x)/((1+3*x)*(1-4*x)). - _Vincenzo Librandi_, Aug 27 2017
%t CoefficientList[Series[(1 + x) / ((1 + 3 x) (1 - 4 x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Aug 27 2017 *)
%o (PARI) a(n) = if (n==1, 1, if (n==2, 2, a(n-1) + 12*a(n-2))); \\ _Michel Marcus_, Jul 25 2017
%o (Magma) [(5/28)*4^n-(2/21)*(-3)^n: n in [1..30]]; // _Vincenzo Librandi_, Aug 27 2017
%Y Cf. A000045, A000079, A133577.
%K nonn,easy
%O 1,2
%A _Matt C. Anderson_, Jul 20 2017
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