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A253119 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. 9

%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

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Last modified February 9 06:46 EST 2023. Contains 360153 sequences. (Running on oeis4.)