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%I #15 Mar 17 2018 04:03:57
%S 4,22,49,94,169,298,529,958,1777,3370,6505,12718,25081,49738,98977,
%T 197374,394081,787402,1573945,3146926,6292777,12584362,25167409,
%U 50333374,100665169,201328618,402655369,805308718,1610615257,3221228170,6442453825,12884904958
%N Number of irredundant sets in the complete tripartite graph K_{n,n,n}.
%C When n > 1, the nonempty irredundant sets are those consisting of either any number of vertices from a single partition or otherwise exactly two vertices from different partitions. - _Andrew Howroyd_, Aug 10 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite 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) = 3*(2^n + n^2) - 2 for n > 1. - _Andrew Howroyd_, Aug 10 2017
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 5.
%F G.f.: (x (4 + 2 x - 25 x^2 + 19 x^3 - 6 x^4))/((-1 + x)^3 (-1 + 2 x)).
%t Table[If[n == 1, 4, 3 (2^n + n^2) - 2], {n, 20}]
%t Join[{4}, LinearRecurrence[{5, -9, 7, -2}, {22, 49, 94, 169}, 20]]
%t CoefficientList[Series[(4 + 2 x - 25 x^2 + 19 x^3 - 6 x^4)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
%o (PARI) a(n) = if(n==1, 4, 3*(2^n + n^2) - 2); \\ _Andrew Howroyd_, Aug 10 2017
%Y Cf. A290707.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Aug 09 2017
%E a(7)-a(32) from _Andrew Howroyd_, Aug 10 2017
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