A393548 Number of total dominating sets in K_{2n,2n,2n} minus a perfect matching.

39, 3882, 260847, 16770378, 1073708139, 68719317138, 4398045774015, 281474973368562, 18014398494540075, 1152921504540787050, 73786976294548799919, 4722366482868386923002, 302231454903651857859147, 19342813113834043441414818, 1237940039285380175041135359, 79228162514264337168342188898

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Complete Tripartite Graph Minus Perfect Matching.

Eric Weisstein's World of Mathematics, Total Dominating Set.

Index entries for linear recurrences with constant coefficients, signature (75,-747,2825,-4728,3600,-1024).

Formula

From Andrew Howroyd, Feb 21 2026: (Start)

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

G.f.: 3*x*(13 + 319*x - 390*x^2 - 1156*x^3 + 80*x^4)/((1 - x)^3*(1 - 4*x)^2*(1 - 64*x)). (End)

E.g.f.: exp(64*x) - 24*x*exp(4*x) - 3*exp(4*x) + 3*x^2*exp(x) + 9*x*exp(x) + 2*exp(x). - Enrique Navarrete, Feb 21 2026

a(n) = 75*a(n-1)-747*a(n-2)+2825*a(n-3)-4728*a(n-4)+3600*a(n-5)-1024*a(n-6). - Eric W. Weisstein, Feb 21 2026

Mathematica

Table[(4^n - 1)^3 + 3 (4^n - n - 1)^2, {n, 20}] (* Eric W. Weisstein, Feb 21 2026 *)
LinearRecurrence[{75, -747, 2825, -4728, 3600, -1024}, {39, 3882, 260847, 16770378, 1073708139, 68719317138}, 20] (* Eric W. Weisstein, Feb 21 2026 *)
CoefficientList[Series[3 (13 + 319 x - 390 x^2 - 1156 x^3 + 80 x^4)/((-1 + x)^3 (-1 + 4 x)^2 (-1 + 64 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Feb 21 2026 *)

Crossrefs

Cf. A393553.

Sequence in context: A176073 A145619 A027490 * A380153 A323688 A266453

Adjacent sequences: A393545 A393546 A393547 * A393549 A393550 A393551

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 20 2026

Extensions

a(6) onward from Andrew Howroyd, Feb 21 2026

Status

approved