A294240 The number of possible ways in which 2*n^2 black pawns and 2*n^2 white pawns can be arranged on a 2n X 2n chessboard such that no pawn attacks another.

1, 3, 30, 410, 6148, 96120, 1526700, 24425026, 392143828, 6306613690, 101505099104, 1634209596410, 26311180850268, 423567557239604, 6817440328754244, 109703307312544664, 1764863031686159684, 28385338557467333804, 456426743658724223028, 7337464027218416593362

Offset

0,2

Comments

White pawns attack diagonally up and black pawns attack diagonally down.

En passant capturing is not possible.

Links

Table of n, a(n) for n=0..19.

Code Golf Stack Exchange user feersum, Too many pawns on a chess board.

Example

For n = 1 the a(1) = 3 boards are as follows:
  +---+---+    +---+---+    +---+---+
  | W | W |    | B | W |    | W | B |
  +---+---+    +---+---+    +---+---+
  | B | B |    | W | B |    | B | W |
  +---+---+    +---+---+    +---+---+
.
An example of one of the a(2) = 30 boards is:
  +---+---+---+---+
  | W | W | W | W |
  +---+---+---+---+
  | B | W | W | W |
  +---+---+---+---+
  | B | B | W | B |
  +---+---+---+---+
  | B | B | B | B |
  +---+---+---+---+

Crossrefs

Cf. A035290.

Sequence in context: A234506 A212425 A336538 * A007004 A354291 A354287

Adjacent sequences: A294237 A294238 A294239 * A294241 A294242 A294243

Keyword

nonn

Author

Peter Kagey, Oct 25 2017

Status

approved