A292058 Wiener index of the n X n rook complement graph.

0, 10, 54, 168, 400, 810, 1470, 2464, 3888, 5850, 8470, 11880, 16224, 21658, 28350, 36480, 46240, 57834, 71478, 87400, 105840, 127050, 151294, 178848, 210000, 245050, 284310, 328104, 376768, 430650, 490110, 555520, 627264, 705738, 791350, 884520, 985680, 1095274

Offset

1,2

Comments

Sequence extended to a(2) using the formula/recurrence (the graph is disconnected for n = 2).

Links

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Rook Complement Graph.

Eric Weisstein's World of Mathematics, Wiener Index.

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

Formula

a(n) = (n - 1)*n^2*(n + 3)/2.

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

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

From Amiram Eldar, Apr 16 2022: (Start)

Sum_{n>=2} 1/a(n) = 265/216 - Pi^2/9.

Sum_{n>=2} (-1)^n/a(n) = Pi^2/18 + 8*log(2)/9 - 233/216. (End)

Mathematica

Table[(n - 1) n^2 (n + 3)/2, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 10, 54, 168, 400}, 20]
CoefficientList[Series[2 x (-5 - 2 x + x^2)/(-1 + x)^5, {x, 0, 20}], x]

Crossrefs

Sequence in context: A093187 A208616 A219169 * A152762 A161458 A162248

Adjacent sequences: A292055 A292056 A292057 * A292059 A292060 A292061

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved