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A188777 T(n,k)=Number of n-turn bishop's tours on a kXk board summed over all starting positions 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 A100074 A330422

Adjacent sequences:  A188774 A188775 A188776 * A188778 A188779 A188780

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 10 2011

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)