login
A187299
Number of 4-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.
1
0, 0, 54, 196, 480, 876, 1398, 2036, 2790, 3660, 4646, 5748, 6966, 8300, 9750, 11316, 12998, 14796, 16710, 18740, 20886, 23148, 25526, 28020, 30630, 33356, 36198, 39156, 42230, 45420, 48726, 52148, 55686, 59340, 63110, 66996, 70998, 75116, 79350, 83700
OFFSET
1,3
COMMENTS
Row 4 of A187296.
LINKS
FORMULA
Empirical: a(n) = 58*n^2 - 232*n + 180 for n>5.
Conjectures from Colin Barker, Apr 23 2018: (Start)
G.f.: 2*x^3*(27 + 17*x + 27*x^2 - 15*x^3 + 7*x^4 - 5*x^5) / (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:
..1..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....0..0..0..0....0..2..1..0....2..4..3..0
..2..4..3..0....1..3..2..4....4..3..2..0....0..4..0..0....1..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..3..0..0....0..0..0..0
CROSSREFS
Cf. A187296.
Sequence in context: A044980 A248598 A157428 * A288626 A124007 A221867
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved