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, Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (75,-747,2825,-4728,3600,-1024).
FORMULA
From Andrew Howroyd, Feb 20 2026: (Start)
a(n) = (4^n-1)^3 + 3*(4^n-1)^2 - 3*n*(4^n-n-1) + 3.
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)
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
MATHEMATICA
A393553[n_] := 3*(n^2 + n - 4^n*(n+1)) + 64^n + 5;
Array[A393553, 20] (* Paolo Xausa, Feb 23 2026 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Feb 20 2026
EXTENSIONS
a(5) from Christian Sievers, Feb 20 2026
a(6) onward from Andrew Howroyd, Feb 20 2026
STATUS
approved