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a(1)=1, a(n)=n*13^(n-1)+a(n-1).
2

%I #17 Feb 12 2024 06:36:09

%S 1,27,534,9322,152127,2379885,36167548,538155684,7879732173,

%T 113924725903,1630368136242,23136292864686,326011399456939,

%U 4566262891748481,63626908677237816,882601196902689928

%N a(1)=1, a(n)=n*13^(n-1)+a(n-1).

%H Vincenzo Librandi, <a href="/A014928/b014928.txt">Table of n, a(n) for n = 1..900</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27, -195, 169).

%F a(1)=1, a(2)=27, a(n) = 26*a(n-1) -169*a(n-2) +1. - _Vincenzo Librandi_, Oct 23 2012

%F G.f.: x/((1-x)*(1-13*x)^2). - _Vincenzo Librandi_, Oct 23 2012

%F a(1)=1, a(2)=27, a(3)=534, a(n)=27*a(n-1)-195*a(n-2)+169*a(n-3). - _Harvey P. Dale_, Jan 20 2015

%t CoefficientList[Series[1/((1 - x)(1 - 13*x)^2), {x, 0, 900}], x] (* _Vincenzo Librandi_, Oct 23 2012 *)

%t RecurrenceTable[{a[1]==1,a[n]==n*13^(n-1)+a[n-1]},a,{n,20}] (* or *) LinearRecurrence[{27,-195,169},{1,27,534},20] (* _Harvey P. Dale_, Jan 20 2015 *)

%o (Magma) I:=[1, 27]; [n le 2 select I[n] else 26*Self(n-1)-169*Self(n-2)+1: n in [1..20]]; // _Vincenzo Librandi_, Oct 23 2012

%K nonn,easy

%O 1,2

%A _Olivier GĂ©rard_