A172218 Number of ways to place 3 nonattacking nightriders on a 3 X n board.

1, 12, 36, 100, 213, 408, 712, 1148, 1745, 2528, 3524, 4760, 6263, 8060, 10178, 12644, 15485, 18728, 22400, 26528, 31139, 36260, 41918, 48140, 54953, 62384, 70460, 79208, 88655, 98828, 109754, 121460, 133973, 147320, 161528, 176624, 192635

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

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

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

Crossrefs

Cf. A172141, A061989, A172212.

Programs

Mathematica

CoefficientList[Series[(2 x^10 - 4 x^9 + 6 x^8 - 4 x^7 - 6 x^6 + 24 x^5 - 18 x^4 + 24 x^3 - 6 x^2 + 8 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (9n^3 - 57n^2 + 210n - 344)/2, n>=8.

G.f.: x*(2*x^10-4*x^9+6*x^8-4*x^7-6*x^6+24*x^5-18*x^4+24*x^3-6*x^2+8*x+1)/(x-1)^4. - Vaclav Kotesovec, Mar 25 2010