A187608 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

0, 0, 0, 28, 144, 340, 675, 1120, 1675, 2340, 3115, 4000, 4995, 6100, 7315, 8640, 10075, 11620, 13275, 15040, 16915, 18900, 20995, 23200, 25515, 27940, 30475, 33120, 35875, 38740, 41715, 44800, 47995, 51300, 54715, 58240, 61875, 65620, 69475, 73440, 77515

Offset

1,4

Comments

Row 4 of A187606.

Links

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

Formula

Empirical: a(n) = 55*n^2 - 380*n + 640 for n>5.

Conjectures from Colin Barker, Apr 25 2018: (Start)

G.f.: x^4*(28 + 60*x - 8*x^2 + 59*x^3 - 29*x^4) / (1 - x)^3.

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

(End)

Example

Some solutions for 5 X 5:
..0..0..0..0..0....0..0..0..1..0....0..0..0..0..4....0..0..2..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..3..0..0....1..0..0..4..0
..0..0..2..0..0....0..0..2..0..0....0..0..0..2..0....0..3..0..0..0
..1..0..0..4..0....0..0..0..4..0....0..0..0..0..1....0..0..0..0..0
..0..0..0..0..3....0..0..0..0..3....0..0..0..0..0....0..0..0..0..0

Crossrefs

Cf. A187606.

Sequence in context: A317680 A042530 A042532 * A069917 A028380 A219887

Adjacent sequences: A187605 A187606 A187607 * A187609 A187610 A187611

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved