

A187607


Number of 3step one space for components leftwards or up, two space for components rightwards or down asymmetric quasibishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.


1



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
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OFFSET

1,3


COMMENTS



LINKS



FORMULA

Empirical: a(n) = 16*n^2  80*n + 100 for n>3.
G.f.: x^3*(9 + 9*x + 19*x^2  5*x^3) / (1  x)^3.
a(n) = 3*a(n1)  3*a(n2) + a(n3) 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



KEYWORD

nonn


AUTHOR



STATUS

approved



