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a(n) = 4^n + 3^(n + 1) - 2.
1

%I #21 Sep 08 2022 08:46:19

%S 11,41,143,497,1751,6281,22943,85217,321191,1225721,4725743,18371537,

%T 71891831,282784361,1116788543,4424107457,17567289671,69881738201,

%U 278364691343,1109971980977,4429427570711,17686329223241,70651173714143,282322265320097,1128441772670951

%N a(n) = 4^n + 3^(n + 1) - 2.

%C Number of dominating sets in the n-book graph.

%H Vincenzo Librandi, <a href="/A288795/b288795.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BookGraph.html">Book Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).

%F a(n) = 4^n + 3^(n + 1) - 2.

%F a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3).

%F G.f.: -((x*(11 - 47*x + 24*x^2))/((-1 + x)*(-1 + 3*x)*(-1 + 4*x))).

%t Table[4^n + 3^(n + 1) - 2, {n, 20}]

%t LinearRecurrence[{8, -19, 12}, {11, 41, 143}, 20]

%t CoefficientList[Series[-((11 - 47 x + 24 x^2)/((-1 + x) (-1 + 3 x) (-1 + 4 x))), {x, 0, 20}], x]

%o (Magma) [4^n+3^(n+1)-2: n in [1..30]]; // _Vincenzo Librandi_, Jun 30 2017

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jun 29 2017