A187607 Number of 3-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, 9, 36, 100, 196, 324, 484, 676, 900, 1156, 1444, 1764, 2116, 2500, 2916, 3364, 3844, 4356, 4900, 5476, 6084, 6724, 7396, 8100, 8836, 9604, 10404, 11236, 12100, 12996, 13924, 14884, 15876, 16900, 17956, 19044, 20164, 21316, 22500, 23716, 24964

Offset

1,3

Comments

Row 3 of A187606.

Links

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

Formula

Empirical: a(n) = 16*n^2 - 80*n + 100 for n>3.

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

G.f.: x^3*(9 + 9*x + 19*x^2 - 5*x^3) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

Example

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

Crossrefs

Cf. A187606.

Sequence in context: A231670 A134537 A066647 * A231674 A085037 A231678

Adjacent sequences: A187604 A187605 A187606 * A187608 A187609 A187610

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved