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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A010797 A260784

Adjacent sequences:  A187849 A187850 A187851 * A187853 A187854 A187855

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 14 2011

STATUS

approved

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Last modified October 25 03:24 EDT 2021. Contains 348235 sequences. (Running on oeis4.)