A187291 Number of 6-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 0, 1440, 15424, 57288, 134408, 248208, 397152, 580328, 797160, 1047532, 1331408, 1648788, 1999672, 2384060, 2801952, 3253348, 3738248, 4256652, 4808560, 5393972, 6012888, 6665308, 7351232, 8070660, 8823592, 9610028, 10429968, 11283412

Offset

1,3

Comments

Row 6 of A187286.

Links

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

Formula

Empirical: a(n) = 16752*n^2 - 101420*n + 136160 for n>9.

Conjectures from Colin Barker, Apr 22 2018: (Start)

G.f.: 4*x^3*(360 + 2776*x + 3834*x^2 + 1844*x^3 + 356*x^4 - 384*x^5 - 228*x^6 - 144*x^7 - 29*x^8 - 9*x^9) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)

Example

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

Crossrefs

Cf. A187286.

Sequence in context: A157508 A061221 A238041 * A187193 A223108 A023102

Adjacent sequences: A187288 A187289 A187290 * A187292 A187293 A187294

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved