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A199109 a(n) = (7*3^n + 1)/2.

%I A199109 #43 Apr 02 2025 19:02:11
%S A199109 4,11,32,95,284,851,2552,7655,22964,68891,206672,620015,1860044,
%T A199109 5580131,16740392,50221175,150663524,451990571,1355971712,4067915135,
%U A199109 12203745404,36611236211,109833708632,329501125895,988503377684,2965510133051,8896530399152,26689591197455
%N A199109 a(n) = (7*3^n + 1)/2.
%C A199109 Also the number of (not necessarily maximal) cliques in the (n+2)-Mycielski graph. - _Eric W. Weisstein_, Nov 29 2017
%H A199109 Vincenzo Librandi, <a href="/A199109/b199109.txt">Table of n, a(n) for n = 0..1000</a>
%H A199109 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>.
%H A199109 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MycielskiGraph.html">Mycielski Graph</a>.
%H A199109 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A199109 a(n) = 3*a(n-1) - 1.
%F A199109 a(n) = 4*a(n-1) - 3*a(n-2).
%F A199109 G.f.: (4-5*x)/((1-x)*(1-3*x)). - _Bruno Berselli_, Nov 03 2011
%F A199109 a(n) = A000244(n+1) + A003462(n) + 1 = A237930(n) + 1. - _Philippe Deléham_, Feb 16 2014
%F A199109 From _Elmo R. Oliveira_, Apr 02 2025: (Start)
%F A199109 E.g.f.: exp(x)*(7*exp(2*x) + 1)/2.
%F A199109 a(n) = A199110(n)/2. (End)
%e A199109 Ternary....................Decimal
%e A199109 11...............................4
%e A199109 102.............................11
%e A199109 1012............................32
%e A199109 10112...........................95
%e A199109 101112.........................284
%e A199109 1011112........................851
%e A199109 10111112......................2552
%e A199109 101111112.....................7655
%e A199109 1011111112...................22964, etc.
%e A199109 - _Philippe Deléham_, Feb 16 2014
%t A199109 Table[(7 3^n + 1)/2, {n, 0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A199109 (7 3^Range[0, 20] + 1)/2 (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A199109 LinearRecurrence[{4, -3}, {11, 32}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A199109 CoefficientList[Series[(4 - 5 x)/(1 - 4 x + 3 x^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)
%o A199109 (Magma) [(7*3^n+1)/2 : n in [0..30]];
%o A199109 (PARI) a(n)=7*3^n\2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A199109 Cf. A000244, A003462, A005032 (first differences), A199110, A237930.
%K A199109 nonn,easy
%O A199109 0,1
%A A199109 _Vincenzo Librandi_, Nov 03 2011