Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Sep 27 2015 12:21:13
%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