

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
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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



