A187292 Number of 7-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 0, 2304, 47648, 228512, 616752, 1241936, 2102944, 3192912, 4505424, 6037932, 7789392, 9759616, 11948560, 14356224, 16982608, 19827712, 22891536, 26174080, 29675344, 33395328, 37334032, 41491456, 45867600, 50462464, 55276048, 60308352

Offset: 1

Author

R. H. Hardin, Mar 08 2011

Keywords

• nonn

Comments

Row 7 of A187286.

Examples

			Some solutions for 4 X 4:
..0..0..0..0....0..0..0..0....0..1..0..0....2..3..0..0....6..5..7..0
..0..5..6..4....0..0..7..0....3..2..7..0....1..5..7..6....0..0..0..0
..1..2..0..3....4..1..5..0....5..0..6..0....0..4..0..0....0..4..0..3
..0..0..7..0....3..2..6..0....4..0..0..0....0..0..0..0....0..1..0..2
		

Links

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

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 109360*n^2 - 763776*n + 1206864 for n>11.

Conjectures from Colin Barker, Apr 23 2018: (Start)

G.f.: 4*x^3*(576 + 10184*x + 23120*x^2 + 17964*x^3 + 7392*x^4 - 280*x^5 - 1716*x^6 - 1604*x^7 - 637*x^8 - 261*x^9 - 47*x^10 - 11*x^11) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

(End)