A187291 Number of 6-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 0, 1440, 15424, 57288, 134408, 248208, 397152, 580328, 797160, 1047532, 1331408, 1648788, 1999672, 2384060, 2801952, 3253348, 3738248, 4256652, 4808560, 5393972, 6012888, 6665308, 7351232, 8070660, 8823592, 9610028, 10429968, 11283412

Offset: 1

Author

R. H. Hardin, Mar 08 2011

Keywords

• nonn

Comments

Row 6 of A187286.

Examples

			Some solutions for 4 X 4:
  0 2 1 3    0 0 3 4    0 0 0 0    0 0 1 2    1 2 3 0
  0 0 0 0    0 0 0 0    0 0 0 0    0 5 6 4    0 5 4 0
  0 5 0 4    0 0 2 5    1 2 4 3    0 0 0 3    0 6 0 0
  0 6 0 0    0 0 1 6    0 6 5 0    0 0 0 0    0 0 0 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 16752*n^2 - 101420*n + 136160 for n>9.

Conjectures from Colin Barker, Apr 22 2018: (Start)

G.f.: 4*x^3*(360 + 2776*x + 3834*x^2 + 1844*x^3 + 356*x^4 - 384*x^5 - 228*x^6 - 144*x^7 - 29*x^8 - 9*x^9) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)