A187156 Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 20, 64, 132, 224, 340, 480, 644, 832, 1044, 1280, 1540, 1824, 2132, 2464, 2820, 3200, 3604, 4032, 4484, 4960, 5460, 5984, 6532, 7104, 7700, 8320, 8964, 9632, 10324, 11040, 11780, 12544, 13332, 14144, 14980, 15840, 16724, 17632, 18564, 19520, 20500

Offset

1,3

Comments

Row 3 of A187155.

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

Empirical: a(n) = 12*n^2 - 40*n + 32 for n>1.

Conjectures from Colin Barker, Feb 28 2018: (Start)

G.f.: 4*x^3*(5 + x) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Example

Some solutions for 4 X 4:
..0..0..0..3....0..0..3..0....1..0..0..0....0..1..0..3....0..1..0..0
..0..0..2..0....0..2..0..0....0..2..0..0....0..0..2..0....0..0..2..0
..0..1..0..0....0..0..1..0....3..0..0..0....0..0..0..0....0..3..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

Crossrefs

Cf. A187155.

Sequence in context: A117432 A033577 A262486 * A246877 A074632 A225190

Adjacent sequences: A187153 A187154 A187155 * A187157 A187158 A187159

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved