A188777 T(n,k)=Number of n-turn bishop's tours on a kXk board summed over all starting positions

1, 4, 0, 9, 4, 0, 16, 20, 0, 0, 25, 56, 28, 0, 0, 36, 120, 152, 24, 0, 0, 49, 220, 488, 328, 8, 0, 0, 64, 364, 1192, 1720, 584, 0, 0, 0, 81, 560, 2468, 5816, 5464, 840, 0, 0, 0, 100, 816, 4560, 15424, 26360, 15824, 784, 0, 0, 0, 121, 1140, 7760, 34736, 91120, 112680, 40496

Offset

1,2

Comments

Table starts

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

.0.4.20..56....120.....220......364......560......816.....1140....1540...2024

.0.0.28.152....488....1192.....2468.....4560.....7760....12400...18860..27560

.0.0.24.328...1720....5816....15424....34736....69776...128528..221448.361528

.0.0..8.584...5464...26360....91120...252720...603696..1288592.2525400

.0.0..0.840..15824..112680...516160..1778608..5082912.12622640

.0.0..0.784..40496..451104..2803552.12139552.41792672

.0.0..0.384..88264.1665344.14497784.80088992

.0.0..0...0.159704.5607456

.0.0..0...0.229296

Links

R. H. Hardin, Table of n, a(n) for n = 1..113

Formula

Empirical: T(1,k) = k^2

Empirical: T(2,k) = (4/3)*k^3 - 2*k^2 + (2/3)*k

Empirical: T(3,k) = 4*T(3,k-1)-5*T(3,k-2)+5*T(3,k-4)-4*T(3,k-5)+T(3,k-6)

Empirical: T(4,k) = 4*T(4,k-1)-4*T(4,k-2)-4*T(4,k-3)+10*T(4,k-4)-4*T(4,k-5)-4*T(4,k-6)+4*T(4,k-7)-T(4,k-8)

Empirical: T(5,k) = 4*T(5,k-1)-3*T(5,k-2)-8*T(5,k-3)+14*T(5,k-4)-14*T(5,k-6)+8*T(5,k-7)+3*T(5,k-8)-4*T(5,k-9)+T(5,k-10)

Empirical: T(6,k) = 4*T(6,k-1)-2*T(6,k-2)-12*T(6,k-3)+17*T(6,k-4)+8*T(6,k-5)-28*T(6,k-6)+8*T(6,k-7)+17*T(6,k-8)-12*T(6,k-9)-2*T(6,k-10)+4*T(6,k-11)-T(6,k-12)

Example

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

Crossrefs

Row 2 is A002492(n-1)

Sequence in context: A187155 A187296 A187046 * A016683 A338107 A100074

Adjacent sequences: A188774 A188775 A188776 * A188778 A188779 A188780

Keyword

nonn,tabl

Author

R. H. Hardin Apr 10 2011

Status

approved