A187287 Number of 2-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 8, 36, 80, 140, 216, 308, 416, 540, 680, 836, 1008, 1196, 1400, 1620, 1856, 2108, 2376, 2660, 2960, 3276, 3608, 3956, 4320, 4700, 5096, 5508, 5936, 6380, 6840, 7316, 7808, 8316, 8840, 9380, 9936, 10508, 11096, 11700, 12320, 12956, 13608, 14276, 14960, 15660

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*n^2 - 12*n for n>1.

Empirical g.f.: 4*x^2*(2+3*x-x^2)/(1-x)^3. - Colin Barker, Jan 22 2012

Example

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

Maple

A187287:=n->`if`(n=1, 0, 8*n^2 - 12*n); seq(A187287(n), n=1..50); # Wesley Ivan Hurt, Feb 28 2014

Crossrefs

Row 2 of A187286.

Cf. A014107.

Sequence in context: A139608 A321778 A009923 * A224159 A321251 A035006

Adjacent sequences: A187284 A187285 A187286 * A187288 A187289 A187290

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved