A187612 - OEIS

A187612

Number of 8-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, 0, 0, 474, 3780, 12946, 32869, 68308, 117760, 187311, 275272, 379035, 500919, 639115, 793623, 964443, 1151575, 1355019, 1574775, 1810843, 2063223, 2331915, 2616919, 2918235, 3235863, 3569803, 3920055, 4286619, 4669495, 5068683, 5484183

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

Row 8 of A187606.

LINKS

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

FORMULA

Empirical: a(n) = 8156*n^2 - 114640*n + 385419 for n>13.

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

G.f.: x^6*(474 + 2358*x + 3028*x^2 + 4897*x^3 + 4759*x^4 - 1503*x^5 + 6086*x^6 - 1689*x^7 - 2608*x^8 + 2319*x^9 - 1809*x^10) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>16.