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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. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 3 of A187606.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2011
STATUS
approved

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Last modified June 18 08:27 EDT 2024. Contains 373472 sequences. (Running on oeis4.)