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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 22 10:24 EDT 2017. Contains 289669 sequences.