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%I #7 Sep 27 2015 12:21:10
%S 17,56,56,257,131,257,642,1087,1087,642,1581,2827,9985,2827,1581,2389,
%T 10411,44729,44729,10411,2389,5716,15803,215037,316686,215037,15803,
%U 5716,7691,41139,321383,1432500,1432500,321383,41139,7691,11429,52297,1399041
%N 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.
%C Table starts
%C ....17.....56.....257.......642.......1581........2389.........5716
%C ....56....131....1087......2827......10411.......15803........41139
%C ...257...1087....9985.....44729.....215037......321383......1399041
%C ...642...2827...44729....316686....1432500.....3500244.....20832926
%C ..1581..10411..215037...1432500....9787192....31393746....187516434
%C ..2389..15803..321383...3500244...31393746...118474944...1042904812
%C ..5716..41139.1399041..20832926..187516434..1042904812..10608304158
%C ..7691..52297.2045480..31561966..402193875..2922532457..31966946561
%C .11429.111085.4026041.110467360.1885771797.14945980504.220223373747
%C .13229.130089.4462239.138633628.2402676252.26001285048.451565510308
%H R. H. Hardin, <a href="/A253424/b253424.txt">Table of n, a(n) for n = 1..837</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 17] for n>21
%F k=2: [order 9] for n>15
%F k=3: [same order 17] for n>25
%F k=4: [same order 9] for n>21
%F k=5: [same order 17] for n>35
%F k=6: [same order 9] for n>37
%F k=7: [same order 17] for n>55
%F Empirical quasipolynomials for column k:
%F k=1: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>4
%F k=2: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>6
%F k=3: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>8
%F k=4: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>12
%F k=5: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>18
%F k=6: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 2 for n>28
%F k=7: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 4 for n>38
%e Some solutions for n=2 k=4
%e ..0..2..2..3..1..2....0..2..2..3..1..2....0..3..2..2..1..3....0..3..1..2..2..2
%e ..3..3..1..2..2..3....2..3..1..2..2..3....2..3..1..2..3..3....2..3..1..2..2..3
%e ..1..1..3..2..2..2....2..1..3..2..2..2....2..1..3..2..2..2....2..1..3..2..2..2
%e ..4..2..2..1..2..3....4..1..3..2..2..3....4..1..2..2..2..3....4..1..3..2..2..3
%e Knight distance matrix for n=2
%e ..0..3..2..3..2..3
%e ..3..4..1..2..3..4
%e ..2..1..4..3..2..3
%e ..5..2..3..2..3..4
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 31 2014
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