A172529 Number of ways to place 2 nonattacking knights on an n X n toroidal board.

0, 2, 18, 88, 200, 486, 980, 1760, 2916, 4550, 6776, 9720, 13520, 18326, 24300, 31616, 40460, 51030, 63536, 78200, 95256, 114950, 137540, 163296, 192500, 225446, 262440, 303800, 349856, 400950, 457436, 519680, 588060, 662966, 744800, 833976, 930920, 1036070

Offset

1,2

Links

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

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

Formula

a(n) = n^2*(n+3)*(n-3)/2, n>=5.

G.f.: 2*x^2*(16*x^7-71*x^6+121*x^5-98*x^4+40*x^3-9*x^2-4*x-1)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[2 x (16 x^7 - 71 x^6 + 121 x^5 - 98 x^4 + 40 x^3 - 9 x^2 - 4 x - 1) / (x - 1)^5, {x, 0, 50}], x] ( * Vincenzo Librandi, May 29 2013 *)

Crossrefs

Cf. A172132, A172517.

Sequence in context: A360301 A070171 A357757 * A201236 A206623 A036800

Adjacent sequences: A172526 A172527 A172528 * A172530 A172531 A172532

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

Status

approved