

A253424


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 1, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.


9



17, 56, 56, 257, 131, 257, 642, 1087, 1087, 642, 1581, 2827, 9985, 2827, 1581, 2389, 10411, 44729, 44729, 10411, 2389, 5716, 15803, 215037, 316686, 215037, 15803, 5716, 7691, 41139, 321383, 1432500, 1432500, 321383, 41139, 7691, 11429, 52297, 1399041
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OFFSET

1,1


COMMENTS

Table starts
....17.....56.....257.......642.......1581........2389.........5716
....56....131....1087......2827......10411.......15803........41139
...257...1087....9985.....44729.....215037......321383......1399041
...642...2827...44729....316686....1432500.....3500244.....20832926
..1581..10411..215037...1432500....9787192....31393746....187516434
..2389..15803..321383...3500244...31393746...118474944...1042904812
..5716..41139.1399041..20832926..187516434..1042904812..10608304158
..7691..52297.2045480..31561966..402193875..2922532457..31966946561
.11429.111085.4026041.110467360.1885771797.14945980504.220223373747
.13229.130089.4462239.138633628.2402676252.26001285048.451565510308


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..837


FORMULA

Empirical for column k:
k=1: [linear recurrence of order 17] for n>21
k=2: [order 9] for n>15
k=3: [same order 17] for n>25
k=4: [same order 9] for n>21
k=5: [same order 17] for n>35
k=6: [same order 9] for n>37
k=7: [same order 17] for n>55
Empirical quasipolynomials for column k:
k=1: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>4
k=2: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>6
k=3: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>8
k=4: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>12
k=5: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>18
k=6: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>28
k=7: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>38


EXAMPLE

Some solutions for n=2 k=4
..0..2..2..3..1..2....0..2..2..3..1..2....0..3..2..2..1..3....0..3..1..2..2..2
..3..3..1..2..2..3....2..3..1..2..2..3....2..3..1..2..3..3....2..3..1..2..2..3
..1..1..3..2..2..2....2..1..3..2..2..2....2..1..3..2..2..2....2..1..3..2..2..2
..4..2..2..1..2..3....4..1..3..2..2..3....4..1..2..2..2..3....4..1..3..2..2..3
Knight distance matrix for n=2
..0..3..2..3..2..3
..3..4..1..2..3..4
..2..1..4..3..2..3
..5..2..3..2..3..4


CROSSREFS

Sequence in context: A158968 A072895 A097059 * A253417 A117390 A141841
Adjacent sequences: A253421 A253422 A253423 * A253425 A253426 A253427


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Dec 31 2014


STATUS

approved



