A172212 Number of ways to place 3 nonattacking knights on a 3 X n board.

1, 12, 36, 100, 233, 456, 796, 1280, 1935, 2788, 3866, 5196, 6805, 8720, 10968, 13576, 16571, 19980, 23830, 28148, 32961, 38296, 44180, 50640, 57703, 65396, 73746, 82780, 92525, 103008, 114256, 126296, 139155, 152860, 167438, 182916, 199321

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

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. A172134, A061989, A047659, A172202.

Programs

Mathematica

CoefficientList[Series[(6 x^6 - 8 x^5 + 2 x^4 + 24 x^3 - 6 x^2 + 8 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Formula

a(n) = (9n^3 - 45n^2 + 122n - 144)/2, n>=4.

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