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A187300
Number of 5-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, 90, 416, 1208, 2400, 4092, 6208, 8766, 11752, 15166, 19008, 23278, 27976, 33102, 38656, 44638, 51048, 57886, 65152, 72846, 80968, 89518, 98496, 107902, 117736, 127998, 138688, 149806, 161352, 173326, 185728, 198558, 211816, 225502, 239616
OFFSET
1,3
COMMENTS
Row 5 of A187296.
LINKS
FORMULA
Empirical: a(n) = 214*n^2 - 1080*n + 1152 for n>7.
Conjectures from Colin Barker, Apr 23 2018: (Start)
G.f.: 2*x^3*(45 + 73*x + 115*x^2 - 33*x^3 + 50*x^4 - 38*x^5 + 9*x^6 - 7*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)
EXAMPLE
Some solutions for 4 X 4:
..0..0..0..0....0..4..3..2....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..2..1....0..0..0..1....5..4..3..0....5..1..0..0....3..0..4..0
..0..0..0..0....0..5..0..0....0..0..2..0....4..0..0..0....2..0..0..0
..0..4..3..5....0..0..0..0....0..0..1..0....3..2..0..0....1..0..5..0
CROSSREFS
Cf. A187296.
Sequence in context: A234984 A158490 A304618 * A237129 A250870 A284845
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved