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%I #30 Oct 28 2023 09:36:18
%S 0,1,1,0,4,0,1,9,9,1,0,25,0,25,0,1,64,121,121,64,1,0,169,0,1296,0,169,
%T 0,1,441,1681,9025,9025,1681,441,1,0,1156,0,78961,0,78961,0,1156,0,1,
%U 3025,23409,609961,1399489,1399489,609961,23409,3025,1
%N T(n,k) = Number of n X k array permutations with each element moved by a city block distance of one.
%C Relation to A099390: where two tilings align, they define a swap; where two tilings cross, they define a cycle.
%H R. H. Hardin, <a href="/A189245/b189245.txt">Table of n, a(n) for n = 1..241</a>
%e Table starts
%e 0, 1, 0, 1, 0, 1, 0
%e 1, 4, 9, 25, 64, 169, 441
%e 0, 9, 0, 121, 0, 1681, 0
%e 1, 25, 121, 1296, 9025, 78961, 609961
%e 0, 64, 0, 9025, 0, 1399489, 0
%e 1, 169, 1681, 78961, 1399489, 45265984, 994077841
%e 0, 441, 0, 609961, 0, 994077841, 0
%e 1,1156, 23409, 5040025, 219750976, 27918733921, 1671065533809
%e 0,3025, 0, 40144896, 0, 669109276081, 0
%e 1,7921,326041,326199721,34566618241.17750489675689,2827635608217289
%e Some.solutions for 4 X 4:
%e ..4..5..3..2....4..0..3..2....1..2..6..7....4..0..3..7....1..2..3..7
%e ..0..1..7..6....5..1..7..6....0..4..5..3....5..1..2..6....0..9.10..6
%e ..9.10.14.15...12.13.11.10...12.10.11.15....9..8.11.15....4..5.14.15
%e ..8.12.13.11....8..9.15.14....8..9.13.14...13.12.10.14....8.12.13.11
%o (PARI) T(n, k) = abs(polresultant(polchebyshev(n, 2, x/2), polchebyshev(k, 2, I*x/2))); \\ _Seiichi Manyama_, Oct 28 2023
%Y Square of A099390.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, with A099390 interpretative help from William Keith in the Sequence Fans Mailing List, Apr 19 2011
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