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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. 1
642, 2827, 44729, 316686, 1432500, 3500244, 20832926, 31561966, 110467360, 138633628, 354021418, 407664150, 876980034, 965635182, 1845670842, 1978943526, 3471423154, 3658918494, 6009462826, 6260785942, 9758924834, 10083680846 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 7 15:48 EDT 2021. Contains 343651 sequences. (Running on oeis4.)