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A172141 Number of ways to place 2 nonattacking nightriders on an n X n board. 8
0, 6, 28, 96, 240, 518, 980, 1712, 2784, 4310, 6380, 9136, 12688, 17206, 22820, 29728, 38080, 48102, 59964, 73920, 90160, 108966, 130548, 155216, 183200, 214838, 250380, 290192, 334544, 383830, 438340, 498496, 564608, 637126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.

REFERENCES

Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p.829

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

FORMULA

Explicit formula (Christian Poisson, 1990): a(n) = n(3n^3 - 5n^2 + 9n - 4)/6 if n is even and a(n) = n(n - 1)(3n^2 - 2n + 7)/6 if n is odd.

G.f.: -2x^2*(x^2+2x+3)(2x^2+x+1)/((x-1)^5*(x+1)^2) [From Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[-2 x (x^2 + 2 x + 3) (2 x^2 + x + 1) / ((x - 1)^5 (x + 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

A036464, A172123, A172132, A172137.

Sequence in context: A091321 A125310 A138874 * A172132 A011856 A276041

Adjacent sequences:  A172138 A172139 A172140 * A172142 A172143 A172144

KEYWORD

easy,nonn

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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Last modified December 11 21:00 EST 2019. Contains 329937 sequences. (Running on oeis4.)