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A194487 revision #4

A194487

Number of ways to arrange 3 nonattacking knights on the lower triangle of an nXn board

0, 1, 12, 62, 253, 804, 2136, 4958, 10376, 20013, 36144, 61846, 101163, 159286, 242748, 359634, 519806, 735143, 1019796, 1390458, 1866649, 2471016, 3229648, 4172406, 5333268, 6750689, 8467976, 10533678, 13001991, 15933178, 19394004

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

OFFSET

1,3

COMMENTS

Column 3 of A194492

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (17/16)*n^4 + (133/48)*n^3 + (433/24)*n^2 - (743/6)*n + 218 for n>4

EXAMPLE

Some solutions for 3X3

..1......0......1......1......0......0......1......0......0......0......1

..0.1....1.1....1.1....1.0....0.1....0.1....0.1....1.0....1.1....0.0....0.0

..1.0.0..1.0.0..0.0.0..1.0.0..0.1.1..1.0.1..0.0.1..1.1.0..0.1.0..1.1.1..1.0.1

CROSSREFS

Sequence in context: A045822 A065595 A267472 * A196312 A196285 A196335

Adjacent sequences: A194484 A194485 A194486 * A194488 A194489 A194490

KEYWORD

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Aug 26 2011

STATUS

approved