A253342 T(n,k)=Number of (n+2)X(k+2) nonnegative integer arrays with all values the knight distance from the upper left minus as much as 3, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.

69, 488, 488, 1928, 2028, 1928, 7494, 11581, 11581, 7494, 27015, 59519, 100512, 59519, 27015, 87621, 306822, 722826, 722826, 306822, 87621, 319172, 1472184, 5136108, 7184212, 5136108, 1472184, 319172, 945613, 7426426, 32653458, 65795210

Offset

1,1

Comments

Table starts

......69.......488........1928..........7494...........27015.............87621

.....488......2028.......11581.........59519..........306822...........1472184

....1928.....11581......100512........722826.........5136108..........32653458

....7494.....59519......722826.......7184212........65795210.........621408160

...27015....306822.....5136108......65795210.......900035309.......11880244815

...87621...1472184....32653458.....621408160.....11880244815......198343663311

..319172...7426426...237047904....6203113283....143441370184.....3788905574401

..945613..30066852..1348380871...46327921378...1729766633007....65148353195615

.2874539.142944394..8419903755..431150608201..22265080961901...946743614051298

.6935762.470066369.34660596075.2513803675142.168952079085709.12716755528646645

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: [linear recurrence of order 49] for n>66

k=2: [order 25] for n>43

k=3: [order 49] for n>71

k=4: [order 25] for n>55

k=5: [order 49] for n>91

k=6: [order 25] for n>93

Empirical quasipolynomials for column k:

k=1: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 4 for n>17

k=2: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 2 for n>18

k=3: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 4 for n>32

k=4: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 2 for n>30

k=5: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 4 for n>42

k=6: polynomial of degree 12 plus a quasipolynomial of degree 11 with period 2 for n>68

Example

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

Crossrefs

Sequence in context: A262456 A161486 A236158 * A253335 A234832 A234825

Adjacent sequences: A253339 A253340 A253341 * A253343 A253344 A253345

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2014

Status

approved