A302942 - OEIS

%I #5 Feb 16 2025 08:33:53

%S 0,4,54,490,4050,32674,261954,2096770,16776450,134216194,1073738754,

%T 8589928450,68719464450,549755789314,4398046461954,35184371990530,

%U 281474976514050,2251799813292034,18014398508695554,144115188074283010,1152921504603701250,9223372036848484354

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

%C a(n) is also the number of total dominating sets in the complete tripartite graph K_{n,n,n} for n > 0.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-26,16).

%F a(n) = A291703(n) for n > 1.

%F a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3).

%F G.f.: -2*x*(2 + 5*x)/(-1 + 11*x - 26*x^2 + 16*x^3).

%t Table[(2^n - 1)^2 (2^n + 2), {n, 0, 30}]

%t LinearRecurrence[{11, -26, 16}, {4, 54, 490}, {0, 20}]

%t CoefficientList[Series[-((2 x (2 + 5 x))/(-1 + 11 x - 26 x^2 + 16 x^3)), {x, 0, 20}], x]

%Y Cf. A291703.

%K nonn,changed

%O 0,2

%A _Eric W. Weisstein_, Apr 16 2018