login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292058 Wiener index of the n X n rook complement graph. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 6 04:30 EDT 2022. Contains 357261 sequences. (Running on oeis4.)