A391632 - OEIS

%I #23 Feb 16 2026 09:05:56

%S 4,21,127,749,4455,26725,161007,971613,5866487,35426517,213940607,

%T 1291991757,7802356615,47118492485,284548794383

%N Number of mutual-visibility sets in the n-Andrásfai graph.

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

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

%F Conjectured g.f.: x*(4 - 19*x + 33*x^2 - 40*x^3 + 8*x^4)/(1 - 10*x + 29*x^2 - 32*x^3 + 8*x^4). - _Andrew Howroyd_, Jan 12 2026

%t Join[{4}, RootSum[8 - 32 # + 29 #^2 - 10 #^3 + #^4 &, #^Range[2, 15] (8 - 7 # + #^2) &]/4] (* _Eric W. Weisstein_, Feb 16 2026 *)

%t Join[{4}, Table[RootSum[8 - 32 # + 29 #^2 - 10 #^3 + #^4 &, 8 #^n - 7 #^(n + 1) + #^(n + 2) &]/4, {n, 2, 15}]] (* _Eric W. Weisstein_, Feb 16 2026 *)

%t ReplacePart[LinearRecurrence[{10, -29, 32, -8}, {3, 21, 127, 749}, 15], 1 -> 4] (* _Eric W. Weisstein_, Feb 16 2026 *)

%t CoefficientList[Series[(4 - 19 x + 33 x^2 - 40 x^3 + 8 x^4)/(1 - 10 x + 29 x^2 - 32 x^3 + 8 x^4), {x, 0, 14}], x] (* _Eric W. Weisstein_, Feb 16 2026 *)

%K nonn,more

%O 1,1

%A _Eric W. Weisstein_, Dec 14 2025

%E a(10)-a(12) from _Andrew Howroyd_, Jan 12 2026

%E a(13)-a(15) from _Andrew Howroyd_, Jan 20 2026