A253422 Number of (n+2)X(6+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.

2389, 15803, 321383, 3500244, 31393746, 118474944, 1042904812, 2922532457, 14945980504, 26001285048, 158392250101, 207801585533, 793557977083, 925795581422, 2519938337350, 2771810154473, 6319718455926, 6746139806975

Offset

1,1

Comments

Column 6 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>37.

Empirical for n mod 2 = 0: a(n) = 1205993472*n^4 - (163631318528/3)*n^3 + (2066136710043/2)*n^2 - (28779682481989/3)*n + 36218599097803 for n>28.

Empirical for n mod 2 = 1: a(n) = 1205993472*n^4 - (149159396864/3)*n^3 + (1739269789595/2)*n^2 - (22635744758878/3)*n + (53641243448399/2) for n>28.

Example

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

Crossrefs

Sequence in context: A172841 A172752 A020428 * A100974 A279538 A098680

Adjacent sequences: A253419 A253420 A253421 * A253423 A253424 A253425

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved