A189245 T(n,k) = Number of n X k array permutations with each element moved by a city block distance of one.

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, 0, 1, 441, 1681, 9025, 9025, 1681, 441, 1, 0, 1156, 0, 78961, 0, 78961, 0, 1156, 0, 1, 3025, 23409, 609961, 1399489, 1399489, 609961, 23409, 3025, 1

Offset

1,5

Comments

Relation to A099390: where two tilings align, they define a swap; where two tilings cross, they define a cycle.

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Example

Table starts
  0,   1,     0,        1,          0,             1,               0
  1,   4,     9,       25,         64,           169,             441
  0,   9,     0,      121,          0,          1681,               0
  1,  25,   121,     1296,       9025,         78961,          609961
  0,  64,     0,     9025,          0,       1399489,               0
  1, 169,  1681,    78961,    1399489,      45265984,       994077841
  0, 441,     0,   609961,          0,     994077841,               0
  1,1156, 23409,  5040025,  219750976,   27918733921,   1671065533809
  0,3025,     0, 40144896,          0,  669109276081,               0
  1,7921,326041,326199721,34566618241.17750489675689,2827635608217289
Some.solutions for 4 X 4:
..4..5..3..2....4..0..3..2....1..2..6..7....4..0..3..7....1..2..3..7
..0..1..7..6....5..1..7..6....0..4..5..3....5..1..2..6....0..9.10..6
..9.10.14.15...12.13.11.10...12.10.11.15....9..8.11.15....4..5.14.15
..8.12.13.11....8..9.15.14....8..9.13.14...13.12.10.14....8.12.13.11

Prog

(PARI) T(n, k) = abs(polresultant(polchebyshev(n, 2, x/2), polchebyshev(k, 2, I*x/2))); \\ Seiichi Manyama, Oct 28 2023

Crossrefs

Square of A099390.

Sequence in context: A186761 A199786 A348129 * A342372 A289222 A121301

Adjacent sequences: A189242 A189243 A189244 * A189246 A189247 A189248

Keyword

nonn,tabl

Author

R. H. Hardin, with A099390 interpretative help from William Keith in the Sequence Fans Mailing List, Apr 19 2011

Status

approved