A393478 Number of mutual-visibility sets in the n-Plummer-Toft graph.

54, 81, 138, 247, 462, 889, 1740, 3439, 6834, 13621, 27192, 54331, 108606, 217153, 434244, 868423, 1736778, 3473485, 6946896, 13893715, 27787350, 55574617, 111149148, 222298207, 444596322, 889192549, 1778385000, 3556769899, 7113539694, 14227079281, 28454158452

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = 23 + 53*2^(n - 2) + 3*n for n > 2.

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

G.f.: x*(-54+135*x-84*x^2+8*x^3-2*x^4)/((-1+x)^2*(-1+2*x)).

Mathematica

Table[Piecewise[{{54, n == 1}, {81, n == 2}}, 23 + 53 2^(n - 2) + 3 n], {n, 20}]
Join[{54, 81}, LinearRecurrence[{4, -5, 2}, {138, 247, 462}, 20]]
CoefficientList[Series[(-54 + 135 x - 84 x^2 + 8 x^3 - 2 x^4)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A007244 A365262 A114817 * A045005 A043185 A039362

Adjacent sequences: A393475 A393476 A393477 * A393479 A393480 A393481

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 16 2026

Status

approved