A187609 Number of 5-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, 8, 130, 500, 1274, 2372, 3953, 5920, 8273, 11012, 14137, 17648, 21545, 25828, 30497, 35552, 40993, 46820, 53033, 59632, 66617, 73988, 81745, 89888, 98417, 107332, 116633, 126320, 136393, 146852, 157697, 168928, 180545, 192548, 204937

Offset

1,4

Comments

Row 5 of A187606.

Links

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

Formula

Empirical: a(n) = 193*n^2 - 1700*n + 3620 for n>7.

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

G.f.: x^4*(8 + 106*x + 134*x^2 + 156*x^3 - 80*x^4 + 159*x^5 - 97*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

Example

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

Crossrefs

Cf. A187606.

Sequence in context: A239756 A295240 A240630 * A365058 A241076 A349683

Adjacent sequences: A187606 A187607 A187608 * A187610 A187611 A187612

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved