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

1,2

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

Links

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

Formula

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

Example

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

Crossrefs

Row 2 is A108099(n-2)

Sequence in context: A187377 A187155 A187296 * A188777 A016683 A338107

Adjacent sequences: A187043 A187044 A187045 * A187047 A187048 A187049

Keyword

nonn,tabl

Author

R. H. Hardin Mar 02 2011

Status

approved