A253420 Number of (n+2)X(4+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.

642, 2827, 44729, 316686, 1432500, 3500244, 20832926, 31561966, 110467360, 138633628, 354021418, 407664150, 876980034, 965635182, 1845670842, 1978943526, 3471423154, 3658918494, 6009462826, 6260785942, 9758924834, 10083680846

Offset

1,1

Comments

Column 4 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-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) for n>21.

Empirical for n mod 2 = 0: a(n) = (343040/3)*n^4 - 2458368*n^3 + (75723376/3)*n^2 - 139263620*n + 321085542 for n>12.

Empirical for n mod 2 = 1: a(n) = (343040/3)*n^4 - (6002944/3)*n^3 + (52054384/3)*n^2 - (253169804/3)*n + 171953062 for n>12.

Example

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

Crossrefs

Sequence in context: A268840 A230715 A135384 * A289649 A271039 A061324

Adjacent sequences: A253417 A253418 A253419 * A253421 A253422 A253423

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved