A187852 Number of 4-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

0, 24, 1400, 7620, 20952, 41652, 69456, 104268, 146088, 194916, 250752, 313596, 383448, 460308, 544176, 635052, 732936, 837828, 949728, 1068636, 1194552, 1327476, 1467408, 1614348, 1768296, 1929252, 2097216, 2272188, 2454168, 2643156

Offset

1,2

Comments

Row 4 of A187850.

Links

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

Formula

Empirical: a(n) = 3504*n^2 - 17748*n + 21996 for n>5.

Conjectures from Colin Barker, Apr 26 2018: (Start)

G.f.: 4*x^2*(6 + 332*x + 873*x^2 + 567*x^3 + 64*x^4 - 66*x^5 - 24*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Cf. A187850.

Sequence in context: A160310 A269271 A347857 * A276595 A348700 A010797

Adjacent sequences: A187849 A187850 A187851 * A187853 A187854 A187855

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved