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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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