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%I #11 Aug 12 2017 13:02:05
%S 1,4,11,24,47,88,163,304,575,1104,2147,4216,8335,16552,32963,65760,
%T 131327,262432,524611,1048936,2097551,4194744,8389091,16777744,
%U 33555007,67109488,134218403,268436184,536871695,1073742664,2147484547,4294968256,8589935615
%N a(n) = 2^(n+1) + n^2 - 1.
%C For n > 1, also the number of irredundant sets in the complete bipartite graph K_{n,n}.
%C For n > 1, also the number of irredundant sets in the 2 X n rook graph. - _Andrew Howroyd_, Aug 11 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F a(n) = 2^(n+1) + n^2 - 1.
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
%F G.f.: (x (1 - x - 2 x^3))/((-1 + x)^3 (-1 + 2 x)).
%t Table[2^(n + 1) + n^2 - 1, {n, 0, 40}]
%t LinearRecurrence[{5, -9, 7, -2}, {4, 11, 24, 47}, {0, 20}]
%t CoefficientList[Series[(1 - x - 2 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
%o (PARI) a(n)=2^(n+1)+n^2-1 \\ _Charles R Greathouse IV_, Aug 09 2017
%Y Cf. A290709, A290818.
%K nonn,easy
%O 0,2
%A _Eric W. Weisstein_, Aug 09 2017
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