A253419 - OEIS

%I #10 Sep 27 2015 17:43:08

%S 257,1087,9985,44729,215037,321383,1399041,2045480,4026041,4462239,

%T 11268009,13305698,20522668,21502576,42733327,46956630,64753373,

%U 66493567,115073779,122276808,157921612,160638668,253728085,264704952,327391225

%N Number of (n+2)X(3+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 3 of A253424.

%H R. H. Hardin, <a href="/A253419/b253419.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +4*a(n-4) -4*a(n-5) -6*a(n-8) +6*a(n-9) +4*a(n-12) -4*a(n-13) -a(n-16) +a(n-17) for n>25.

%F Empirical for n mod 4 = 0: a(n) = (3008/3)*n^4 - (17836/3)*n^3 + (1507261/48)*n^2 - (2120783/12)*n + 386938 for n>8.

%F Empirical for n mod 4 = 1: a(n) = (3008/3)*n^4 - (14828/3)*n^3 + (1281949/48)*n^2 - (3938669/24)*n + (5831375/16) for n>8.

%F Empirical for n mod 4 = 2: a(n) = (3008/3)*n^4 - (26860/3)*n^3 + (2607325/48)*n^2 - (3154427/12)*n + (2342671/4) for n>8.

%F Empirical for n mod 4 = 3: a(n) = (3008/3)*n^4 - (5804/3)*n^3 - (251267/48)*n^2 - (694613/24)*n + (1836387/16) for n>8.

%e Some solutions for n=2

%e ..0..2..2..2..2....0..2..2..3..2....0..3..2..2..1....0..3..2..2..1

%e ..3..3..1..2..2....2..3..1..2..3....2..3..1..2..3....2..3..1..2..2

%e ..1..1..3..2..2....2..1..3..2..2....2..1..3..2..2....2..1..3..2..2

%e ..4..2..2..1..2....4..1..3..2..3....4..2..3..2..2....4..2..3..2..2

%e Knight distance matrix for n=2

%e ..0..3..2..3..2

%e ..3..4..1..2..3

%e ..2..1..4..3..2

%e ..5..2..3..2..3

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014