%I
%S 53,272,272,1342,920,1342,4619,6334,6334,4619,14541,28600,64228,28600,
%T 14541,34786,139760,426571,426571,139760,34786,113891,502272,2801464,
%U 3950239,2801464,502272,113891,233392,2259097,11529235,28256241,28256241
%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 2, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.
%C Table starts
%C .....53......272.......1342.........4619.........14541...........34786
%C ....272......920.......6334........28600........139760..........502272
%C ...1342.....6334......64228.......426571.......2801464........11529235
%C ...4619....28600.....426571......3950239......28256241.......201911670
%C ..14541...139760....2801464.....28256241.....343085240......3518586637
%C ..34786...502272...11529235....201911670....3518586637.....40022802662
%C .113891..2259097...79249122...1873418602...32095583880....638441329329
%C .233392..5670421..269081698...7421334529..235545304374...7166392767013
%C .525617.21399557.1126140254..54446797689.2365327348752..68323597331510
%C .853971.39120366.2033916546.133685068828.6157835478824.307062940433405
%H R. H. Hardin, <a href="/A253119/b253119.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 33] for n>43
%F k=2: [order 17] for n>29
%F k=3: [same order 33] for n>48
%F k=4: [same order 17] for n>37
%F k=5: [same order 33] for n>63
%F k=6: [same order 17] for n>65
%F Empirical quasipolynomials for column k:
%F k=1: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>10
%F k=2: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>12
%F k=3: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>15
%F k=4: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>20
%F k=5: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>30
%F k=6: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>48
%e Some solutions for n=3 k=4:
%e ..0..1..1..2..1..1....0..1..1..2..1..2....0..1..1..2..1..2....0..1..1..2..1..2
%e ..1..2..0..1..2..2....1..2..0..1..2..2....1..2..0..1..1..2....1..2..0..1..2..2
%e ..1..0..2..1..1..1....1..0..2..2..1..1....1..0..2..1..1..1....1..0..2..1..1..2
%e ..1..0..1..1..1..2....1..1..1..1..1..2....1..1..2..1..2..2....2..0..1..1..2..2
%e ..1..2..1..1..2..2....0..2..1..2..2..1....1..1..1..2..2..1....1..1..1..1..2..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 27 2014
