A187177 Number of 7-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

0, 0, 0, 0, 0, 16, 368, 1600, 4284, 8760, 15104, 23144, 32764, 43944, 56684, 70984, 86844, 104264, 123244, 143784, 165884, 189544, 214764, 241544, 269884, 299784, 331244, 364264, 398844, 434984, 472684, 511944, 552764, 595144, 639084, 684584

Offset

1,6

Comments

Row 7 of A187172.

Links

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

Formula

Empirical: a(n) = 780*n^2 - 9880*n + 29384 for n>11.

G.f.: 4*x^6*(4 + 80*x + 136*x^2 + 143*x^3 + 85*x^4 + 19*x^5 - 43*x^6 - 29*x^7 - 5*x^8) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

Example

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

Crossrefs

Cf. A187172.

Sequence in context: A276097 A265476 A008427 * A053105 A220576 A264186

Adjacent sequences: A187174 A187175 A187176 * A187178 A187179 A187180

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved