A389173 Number of mutual-visibility sets in the n-sun graph.

4, 13, 42, 135, 448, 1505, 5078, 17163, 58044, 196341, 664194, 2246927, 7601272, 25714889, 86992814, 294294547, 995591284, 3368061149, 11394069210, 38545859991, 130399710256, 441139059889, 1492362749830, 5048627019547, 17079382868268, 57779138374085

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Sun Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (5,-6,2,-1,1).

Formula

G.f.: -x*(4-7*x+x^2-5*x^3+3*x^4)/((-1+x)^2*(-1+3*x+x^2+x^3)).

a(n) = 5*a(n-1)-6*a(n-2)+2*a(n-3)-a(n-4)+a(n-5).

Mathematica

Table[n + RootSum[-1 - # - 3 #^2 + #^3 &, #^n &], {n, 20}]
LinearRecurrence[{5, -6, 2, -1, 1}, {4, 13, 42, 135, 448}, 20]
CoefficientList[Series[-(4 - 7 x + x^2 - 5 x^3 + 3 x^4)/((-1 + x)^2 (-1 + 3 x + x^2 + x^3)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A289807 A010919 A022029 * A277667 A274952 A010900

Adjacent sequences: A389170 A389171 A389172 * A389174 A389175 A389176

Keyword

nonn

Author

Eric W. Weisstein, Sep 25 2025

Status

approved