Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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