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%I #10 Sep 27 2015 17:43:42
%S 2389,15803,321383,3500244,31393746,118474944,1042904812,2922532457,
%T 14945980504,26001285048,158392250101,207801585533,793557977083,
%U 925795581422,2519938337350,2771810154473,6319718455926,6746139806975
%N Number of (n+2)X(6+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 Column 6 of A253424.
%H R. H. Hardin, <a href="/A253422/b253422.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) for n>37.
%F Empirical for n mod 2 = 0: a(n) = 1205993472*n^4 - (163631318528/3)*n^3 + (2066136710043/2)*n^2 - (28779682481989/3)*n + 36218599097803 for n>28.
%F Empirical for n mod 2 = 1: a(n) = 1205993472*n^4 - (149159396864/3)*n^3 + (1739269789595/2)*n^2 - (22635744758878/3)*n + (53641243448399/2) for n>28.
%e Some solutions for n=2
%e ..0..3..2..2..2..2..3..4....0..2..2..2..1..2..3..4....0..2..2..3..2..3..3..4
%e ..2..3..1..2..2..3..2..3....3..3..1..2..2..3..2..3....3..3..1..2..3..3..3..3
%e ..2..1..3..3..2..3..3..4....2..1..3..2..1..2..3..4....2..1..3..3..2..2..4..4
%e ..4..2..3..2..3..3..2..3....4..2..2..2..3..3..2..3....4..2..2..2..3..3..3..3
%e Knight distance matrix for n=2
%e ..0..3..2..3..2..3..4..5
%e ..3..4..1..2..3..4..3..4
%e ..2..1..4..3..2..3..4..5
%e ..5..2..3..2..3..4..3..4
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 31 2014
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