A389183 Number of mutual-visibility sets in the n-ladder graph.

4, 15, 41, 94, 190, 349, 595, 956, 1464, 2155, 3069, 4250, 5746, 7609, 9895, 12664, 15980, 19911, 24529, 29910, 36134, 43285, 51451, 60724, 71200, 82979, 96165, 110866, 127194, 145265, 165199, 187120, 211156, 237439, 266105, 297294, 331150, 367821, 407459

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Eric Weisstein's World of Mathematics, Ladder Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n*(13 + 8*n + 2*n^2 + n^3)/6.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).

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

Mathematica

Table[n (13 + 8 n + 2 n^2 + n^3)/6, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 15, 41, 94, 190}, 20]
CoefficientList[Series[(-4 + 5 x - 6 x^2 + x^3)/(-1 + x)^5, {x, 0, 20}], x]

Crossrefs

Sequence in context: A116600 A074033 A093920 * A342352 A011844 A075468

Adjacent sequences: A389180 A389181 A389182 * A389184 A389185 A389186

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 25 2025

Status

approved