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a(n) = 2^n*(n + 1) - 3*(n - 1).
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%I #6 Aug 17 2017 17:32:02

%S 4,9,26,71,180,433,1006,2283,5096,11237,24546,53215,114652,245721,

%T 524246,1114067,2359248,4980685,10485706,22020039,46137284,96468929,

%U 201326526,419430331,872415160,1811939253,3758096306,7784628143,16106127276,33285996457

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

%C For n > 1, also the number of maximal irredundant sets in the n-book graph.

%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/MaximalIrredundantSet.html">Maximal Irredundant Set</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6, -13, 12, -4).

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

%F a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

%F G.f.: (x (4 - 15 x + 24 x^2 - 16 x^3))/(1 - 3 x + 2 x^2)^2.

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

%t LinearRecurrence[{6, -13, 12, -4}, {4, 9, 26, 71, 180}, 20]

%t CoefficientList[Series[(4 - 15 x + 24 x^2 - 16 x^3)/(1 - 3 x + 2 x^2)^2, {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Aug 17 2017