cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A099139 a(n) = (18^n - (-6)^n)/24.

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%I A099139 #13 Dec 31 2023 16:24:45
%S A099139 0,1,12,252,4320,79056,1415232,25520832,459095040,8265390336,
%T A099139 148766948352,2677865536512,48201216860160,867624080265216,
%U A099139 15617220384079872,281110045277601792,5059980344811847680,91079649027723165696,1639433665572357537792,29509806081862392348672
%N A099139 a(n) = (18^n - (-6)^n)/24.
%C A099139 In general k^(n-1)*A015518(n) is given by ((3k)^n-(-k)^n)/(4k) with g.f. x/((1+kx)(1-3kx)).
%H A099139 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,108).
%F A099139 G.f.: x/((1+6x)*(1-18x)).
%F A099139 a(n) = 12a(n-1)+108a(n-2). a(n) = 6^(n-1)*A015518(n).
%t A099139 LinearRecurrence[{12,108},{0,1},20] (* _Harvey P. Dale_, May 24 2015 *)
%Y A099139 Cf. A053524, A053535, A053536, A053537.
%K A099139 easy,nonn
%O A099139 0,3
%A A099139 _Paul Barry_, Sep 29 2004