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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

%I

%S 69,488,488,1928,2028,1928,7494,11581,11581,7494,27015,59519,100512,

%T 59519,27015,87621,306822,722826,722826,306822,87621,319172,1472184,

%U 5136108,7184212,5136108,1472184,319172,945613,7426426,32653458,65795210

%N 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.

%C Table starts

%C ......69.......488........1928..........7494...........27015.............87621

%C .....488......2028.......11581.........59519..........306822...........1472184

%C ....1928.....11581......100512........722826.........5136108..........32653458

%C ....7494.....59519......722826.......7184212........65795210.........621408160

%C ...27015....306822.....5136108......65795210.......900035309.......11880244815

%C ...87621...1472184....32653458.....621408160.....11880244815......198343663311

%C ..319172...7426426...237047904....6203113283....143441370184.....3788905574401

%C ..945613..30066852..1348380871...46327921378...1729766633007....65148353195615

%C .2874539.142944394..8419903755..431150608201..22265080961901...946743614051298

%C .6935762.470066369.34660596075.2513803675142.168952079085709.12716755528646645

%H R. H. Hardin, <a href="/A253342/b253342.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

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

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

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

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

%F Empirical quasipolynomials for column k:

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

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

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

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

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

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

%e Some solutions for n=3 k=4

%e ..0..1..0..1..1..2....0..1..0..1..1..0....0..0..1..1..0..0....0..0..0..0..0..1

%e ..0..1..0..1..1..1....0..1..0..0..1..1....1..1..0..0..1..1....1..1..0..0..0..1

%e ..0..0..1..1..1..1....1..0..1..1..0..1....0..0..1..1..0..1....0..0..1..0..0..0

%e ..0..0..1..0..1..2....1..0..1..0..0..1....0..0..1..1..1..1....0..0..0..0..1..1

%e ..1..0..0..1..2..1....0..1..0..0..2..0....0..1..0..0..2..1....0..0..0..0..1..1

%e Knight distance matrix for n=3

%e ..0..3..2..3..2..3

%e ..3..4..1..2..3..4

%e ..2..1..4..3..2..3

%e ..3..2..3..2..3..4

%e ..2..3..2..3..4..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 30 2014

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Last modified December 1 14:21 EST 2022. Contains 358468 sequences. (Running on oeis4.)