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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 06:49 EDT 2022. Contains 357082 sequences. (Running on oeis4.)