A187292 Number of 7-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 0, 2304, 47648, 228512, 616752, 1241936, 2102944, 3192912, 4505424, 6037932, 7789392, 9759616, 11948560, 14356224, 16982608, 19827712, 22891536, 26174080, 29675344, 33395328, 37334032, 41491456, 45867600, 50462464, 55276048, 60308352

Offset

1,3

Comments

Row 7 of A187286.

Links

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

Formula

Empirical: a(n) = 109360*n^2 - 763776*n + 1206864 for n>11.

Conjectures from Colin Barker, Apr 23 2018: (Start)

G.f.: 4*x^3*(576 + 10184*x + 23120*x^2 + 17964*x^3 + 7392*x^4 - 280*x^5 - 1716*x^6 - 1604*x^7 - 637*x^8 - 261*x^9 - 47*x^10 - 11*x^11) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

(End)

Example

Some solutions for 4 X 4:
..0..0..0..0....0..0..0..0....0..1..0..0....2..3..0..0....6..5..7..0
..0..5..6..4....0..0..7..0....3..2..7..0....1..5..7..6....0..0..0..0
..1..2..0..3....4..1..5..0....5..0..6..0....0..4..0..0....0..4..0..3
..0..0..7..0....3..2..6..0....4..0..0..0....0..0..0..0....0..1..0..2

Crossrefs

Cf. A187286.

Sequence in context: A204102 A177759 A218431 * A235423 A235419 A229698

Adjacent sequences: A187289 A187290 A187291 * A187293 A187294 A187295

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved