A393553 - OEIS

%I #21 Feb 23 2026 16:52:52

%S 51,3975,261417,16773441,1073723487,68719390851,4398046118061,

%T 281474974941405,18014398501617939,1152921504572244303,

%U 73786976294687211921,4722366482868990902745,302231454903654475104807,19342813113834054715703931,1237940039285380223359517397,79228162514264337374500619061

%N Number of dominating sets in K_{2n,2n,2n} minus a perfect matching.

%H Andrew Howroyd, <a href="/A393553/b393553.txt">Table of n, a(n) for n = 1..200</a>

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

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (75,-747,2825,-4728,3600,-1024).

%F From _Andrew Howroyd_, Feb 20 2026: (Start)

%F a(n) = (4^n-1)^3 + 3*(4^n-1)^2 - 3*n*(4^n-n-1) + 3.

%F G.f.: 3*x*(17 + 50*x + 463*x^2 - 2528*x^3 + 1888*x^4 - 1024*x^5)/((1 - x)^3*(1 - 4*x)^2*(1 - 64*x)). (End)

%F E.g.f.: exp(64*x) - 3*(4*x + 1)*exp(4*x) + (3*x^2 + 6*x + 5)*exp(x) - 3. - _Enrique Navarrete_, Feb 21 2026

%t A393553[n_] := 3*(n^2 + n - 4^n*(n+1)) + 64^n + 5;

%t Array[A393553, 20] (* _Paolo Xausa_, Feb 23 2026 *)

%Y Cf. A393548.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Feb 20 2026

%E a(5) from _Christian Sievers_, Feb 20 2026

%E a(6) onward from _Andrew Howroyd_, Feb 20 2026