A343905 Number of ways of placing n nonattacking range-3 leprechauns on an n X n board.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 34, 4, 112, 516, 7312, 81324, 1056560, 13443944, 171919446, 2195838076, 28876216900, 379982087060

Offset

1,16

Comments

First 25 terms were computed by Vaclav Kotesovec in 2020.

A range-k leprechaun is a fairy chess piece that can move to any square within range k, and to any square that a queen can move to (Escamocher and O'Sullivan 2021). A range-1 leprechaun is a queen, a range-2 leprechaun is a superqueen.

Links

Table of n, a(n) for n=1..28.

Guillaume Escamocher and Barry O'Sullivan, Leprechauns on the chessboard, Discrete Mathematics, 344(5), 2021.

Crossrefs

Cf. A000170, A051223, A343907.

Sequence in context: A112980 A109336 A180342 * A232591 A098869 A131544

Adjacent sequences: A343902 A343903 A343904 * A343906 A343907 A343908

Keyword

nonn,more,hard

Author

Guillaume Escamocher, May 03 2021

Extensions

a(26)-a(27) from Martin Ehrenstein, May 06 2021

a(26) confirmed by Vaclav Kotesovec, Jun 07 2021

a(28) from Martin Ehrenstein, Oct 14 2021

Status

approved