

A186851


T(n,k)=Number of nstep knight's tours on a (k+2)X(k+2) board summed over all starting positions


8



9, 16, 16, 25, 48, 16, 36, 96, 104, 16, 49, 160, 328, 208, 16, 64, 240, 664, 976, 400, 16, 81, 336, 1112, 2576, 2800, 800, 16, 100, 448, 1672, 5056, 9328, 8352, 1280, 16, 121, 576, 2344, 8320, 21480, 34448, 21664, 2208, 0, 144, 720, 3128, 12368, 39616, 91328
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Table starts
..9...16.....25......36......49......64......81.....100....121....144...169
.16...48.....96.....160.....240.....336.....448.....576....720....880..1056
.16..104....328.....664....1112....1672....2344....3128...4024...5032..6152
.16..208....976....2576....5056....8320...12368...17200..22816..29216.36400
.16..400...2800....9328...21480...39616...63440...92656.127264.167264
.16..800...8352...34448...91328..186544..322528..498320.712080
.16.1280..21664..118480..372384..847520.1584576.2596480
.16.2208..57392..405040.1508784.3846192.7777808
..0.3184.135184.1290112.5807488
..0.4640.317296.4089632


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..99


FORMULA

Empirical, for all rows: a(n)=3*a(n1)3*a(n2)+a(n3) for n>3,3,4,6,8,10 respectively for row in 1..6


EXAMPLE

Some n=3 solutions for 5X5
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..2..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..1..0..0....0..0..0..0..0....0..0..3..0..0....0..0..0..0..0
..0..0..0..3..0....0..3..0..0..0....2..0..0..0..0....3..0..0..0..1
..0..2..0..0..0....0..0..0..0..0....0..0..1..0..0....0..0..2..0..0


CROSSREFS

Row 2 is A035008
Column 6 is A186441
Sequence in context: A110151 A131746 A092095 * A201266 A231977 A269563
Adjacent sequences: A186848 A186849 A186850 * A186852 A186853 A186854


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin and D. S. McNeil in the Sequence Fans Mailing List, Feb 27 2011


STATUS

approved



