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A187155 T(n,k)=Number of n-step one space at a time bishop's tours on a kXk board summed over all starting positions 7
1, 4, 0, 9, 4, 0, 16, 16, 0, 0, 25, 36, 20, 0, 0, 36, 64, 64, 8, 0, 0, 49, 100, 132, 92, 0, 0, 0, 64, 144, 224, 248, 72, 0, 0, 0, 81, 196, 340, 476, 388, 56, 0, 0, 0, 100, 256, 480, 776, 904, 456, 16, 0, 0, 0, 121, 324, 644, 1148, 1620, 1588, 544, 0, 0, 0, 0, 144, 400, 832, 1592 (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....169.....196

.0.4.16.36..64..100...144...196....256....324....400....484....576.....676

.0.0.20.64.132..224...340...480....644....832...1044...1280...1540....1824

.0.0..8.92.248..476...776..1148...1592...2108...2696...3356...4088....4892

.0.0..0.72.388..904..1620..2536...3652...4968...6484...8200..10116...12232

.0.0..0.56.456.1588..3288..5556...8392..11796..15768..20308..25416...31092

.0.0..0.16.544.2328..6172.11576..18540..27064..37148..48792..61996...76760

.0.0..0..0.472.3504.10576.23340..40448..61900..87696.117836.152320..191148

.0.0..0..0.392.4216.17696.43136..83844.136384.200756.276960.364996..464864

.0.0..0..0.168.5472.26912.80392.168104.296708.457848.651524.877736.1136484

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..287

FORMULA

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

Empirical: T(2,k) = 4*k^2 - 8*k + 4

Empirical: T(3,k) = 12*k^2 - 40*k + 32 for k>1

Empirical: T(4,k) = 36*k^2 - 168*k + 188 for k>2

Empirical: T(5,k) = 100*k^2 - 584*k + 808 for k>3

Empirical: T(6,k) = 284*k^2 - 1992*k + 3316 for k>4

Empirical: T(7,k) = 780*k^2 - 6296*k + 12024 for k>5

Empirical: T(8,k) = 2172*k^2 - 19816*k + 42860 for k>6

EXAMPLE

Some n=4 solutions for 4X4

..0..0..0..1....0..0..1..0....4..0..0..0....0..4..0..0....0..0..1..0

..0..0..2..0....0..2..0..0....0..3..0..0....3..0..1..0....0..2..0..4

..0..3..0..0....0..0..3..0....0..0..2..0....0..2..0..0....0..0..3..0

..0..0..4..0....0..4..0..0....0..0..0..1....0..0..0..0....0..0..0..0

CROSSREFS

Row 2 is A016742(n-1)

Sequence in context: A133844 A198238 A187377 * A187296 A187046 A188777

Adjacent sequences:  A187152 A187153 A187154 * A187156 A187157 A187158

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 06 2011

STATUS

approved

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Last modified December 11 19:09 EST 2017. Contains 295919 sequences.