A187156 Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 20, 64, 132, 224, 340, 480, 644, 832, 1044, 1280, 1540, 1824, 2132, 2464, 2820, 3200, 3604, 4032, 4484, 4960, 5460, 5984, 6532, 7104, 7700, 8320, 8964, 9632, 10324, 11040, 11780, 12544, 13332, 14144, 14980, 15840, 16724, 17632, 18564, 19520, 20500

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 3 of A187155.

Examples

			Some solutions for 4 X 4:
..0..0..0..3....0..0..3..0....1..0..0..0....0..1..0..3....0..1..0..0
..0..0..2..0....0..2..0..0....0..2..0..0....0..0..2..0....0..0..2..0
..0..1..0..0....0..0..1..0....3..0..0..0....0..0..0..0....0..3..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
		

Links

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

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 12*n^2 - 40*n + 32 for n>1.

Conjectures from Colin Barker, Feb 28 2018: (Start)

G.f.: 4*x^3*(5 + x) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)