A253419 Number of (n+2)X(3+2) nonnegative integer arrays with all values the knight distance from the upper left minus as much as 1, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.

257, 1087, 9985, 44729, 215037, 321383, 1399041, 2045480, 4026041, 4462239, 11268009, 13305698, 20522668, 21502576, 42733327, 46956630, 64753373, 66493567, 115073779, 122276808, 157921612, 160638668, 253728085, 264704952, 327391225

Offset

1,1

Comments

Column 3 of A253424.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +4*a(n-4) -4*a(n-5) -6*a(n-8) +6*a(n-9) +4*a(n-12) -4*a(n-13) -a(n-16) +a(n-17) for n>25.

Empirical for n mod 4 = 0: a(n) = (3008/3)*n^4 - (17836/3)*n^3 + (1507261/48)*n^2 - (2120783/12)*n + 386938 for n>8.

Empirical for n mod 4 = 1: a(n) = (3008/3)*n^4 - (14828/3)*n^3 + (1281949/48)*n^2 - (3938669/24)*n + (5831375/16) for n>8.

Empirical for n mod 4 = 2: a(n) = (3008/3)*n^4 - (26860/3)*n^3 + (2607325/48)*n^2 - (3154427/12)*n + (2342671/4) for n>8.

Empirical for n mod 4 = 3: a(n) = (3008/3)*n^4 - (5804/3)*n^3 - (251267/48)*n^2 - (694613/24)*n + (1836387/16) for n>8.

Example

Some solutions for n=2
..0..2..2..2..2....0..2..2..3..2....0..3..2..2..1....0..3..2..2..1
..3..3..1..2..2....2..3..1..2..3....2..3..1..2..3....2..3..1..2..2
..1..1..3..2..2....2..1..3..2..2....2..1..3..2..2....2..1..3..2..2
..4..2..2..1..2....4..1..3..2..3....4..2..3..2..2....4..2..3..2..2
Knight distance matrix for n=2
..0..3..2..3..2
..3..4..1..2..3
..2..1..4..3..2
..5..2..3..2..3

Crossrefs

Sequence in context: A036549 A352983 A031710 * A070184 A054801 A173892

Adjacent sequences: A253416 A253417 A253418 * A253420 A253421 A253422

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved