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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
53, 272, 272, 1342, 920, 1342, 4619, 6334, 6334, 4619, 14541, 28600, 64228, 28600, 14541, 34786, 139760, 426571, 426571, 139760, 34786, 113891, 502272, 2801464, 3950239, 2801464, 502272, 113891, 233392, 2259097, 11529235, 28256241, 28256241 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.....53......272.......1342.........4619.........14541...........34786

....272......920.......6334........28600........139760..........502272

...1342.....6334......64228.......426571.......2801464........11529235

...4619....28600.....426571......3950239......28256241.......201911670

..14541...139760....2801464.....28256241.....343085240......3518586637

..34786...502272...11529235....201911670....3518586637.....40022802662

.113891..2259097...79249122...1873418602...32095583880....638441329329

.233392..5670421..269081698...7421334529..235545304374...7166392767013

.525617.21399557.1126140254..54446797689.2365327348752..68323597331510

.853971.39120366.2033916546.133685068828.6157835478824.307062940433405

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical for column k:

k=1: [linear recurrence of order 33] for n>43

k=2: [order 17] for n>29

k=3: [same order 33] for n>48

k=4: [same order 17] for n>37

k=5: [same order 33] for n>63

k=6: [same order 17] for n>65

Empirical quasipolynomials for column k:

k=1: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>10

k=2: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>12

k=3: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>15

k=4: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>20

k=5: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 4 for n>30

k=6: polynomial of degree 8 plus a quasipolynomial of degree 7 with period 2 for n>48

EXAMPLE

Some solutions for n=3 k=4:

..0..1..1..2..1..1....0..1..1..2..1..2....0..1..1..2..1..2....0..1..1..2..1..2

..1..2..0..1..2..2....1..2..0..1..2..2....1..2..0..1..1..2....1..2..0..1..2..2

..1..0..2..1..1..1....1..0..2..2..1..1....1..0..2..1..1..1....1..0..2..1..1..2

..1..0..1..1..1..2....1..1..1..1..1..2....1..1..2..1..2..2....2..0..1..1..2..2

..1..2..1..1..2..2....0..2..1..2..2..1....1..1..1..2..2..1....1..1..1..1..2..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: A241488 A140851 A337428 * A253112 A211146 A155700

Adjacent sequences: A253116 A253117 A253118 * A253120 A253121 A253122

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 27 2014

STATUS

approved

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Last modified December 4 09:27 EST 2022. Contains 358556 sequences. (Running on oeis4.)