A187046 T(n,k)=Number of n-step one or two space at a time bishop's tours on a kXk board summed over all starting positions.

1, 4, 0, 9, 4, 0, 16, 20, 0, 0, 25, 52, 28, 0, 0, 36, 100, 136, 24, 0, 0, 49, 164, 360, 272, 8, 0, 0, 64, 244, 696, 1084, 456, 0, 0, 0, 81, 340, 1144, 2660, 2896, 584, 0, 0, 0, 100, 452, 1704, 5032, 9216, 6952, 400, 0, 0, 0, 121, 580, 2376, 8164, 20648, 29500, 14024, 80, 0

Offset: 1

Author

R. H. Hardin Mar 02 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1.4..9..16....25......36......49......64......81.....100.....121....144....169

.0.4.20..52...100.....164.....244.....340.....452.....580.....724....884...1060

.0.0.28.136...360.....696....1144....1704....2376....3160....4056...5064...6184

.0.0.24.272..1084....2660....5032....8164...12056...16708...22120..28292..35224

.0.0..8.456..2896....9216...20648...37472...59524...86656..118868.156160.198532

.0.0..0.584..6952...29500...79088..162320..281320..435436..623508.845084

.0.0..0.400.14024...86608..285048..668176.1272720.2110944.3180724

.0.0..0..80.22200..226864..961728.2625640.5543744.9907248

.0.0..0...0.26672..522608.3009408.9817240

.0.0..0...0.22448.1050048.8701592

Examples

			Some n=4 solutions for 4X4
..0..2..0..0....0..4..0..0....0..0..0..0....4..0..0..0....0..3..0..0
..1..0..3..0....0..0..0..0....0..0..3..0....0..3..0..0....0..0..2..0
..0..0..0..4....0..1..0..3....0..0..0..2....0..0..1..0....0..1..0..4
..0..0..0..0....0..0..2..0....4..0..1..0....0..0..0..2....0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Row 2 is A108099(n-2)

Formula

Empirical: Row n is a polynomial of degree 2 for k>2n-3