A209433 Number of chess diagrams that can be obtained in n plies, but not in fewer plies.

1, 20, 400, 5202, 69731, 766337, 8708079, 86540204, 880526165, 7996545696, 73802185449, 616052245142

Offset

0,2

Comments

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. The condition that the diagram cannot be obtained in fewer than n plies means that each legal chess diagram is counted exactly once in this sequence, indexed by the length of the shortest game(s) to reach it. Therefore, this sequence is finite and its sum equals the number of legal chess diagrams, estimated to be between 10^43 and 10^47.

Links

Table of n, a(n) for n=0..11.

F. Labelle, Statistics on chess positions

Index entries for sequences related to number of chess games

Crossrefs

Cf. A019319, A209080.

Sequence in context: A207091 A223988 A189698 * A188988 A019319 A083276

Adjacent sequences: A209430 A209431 A209432 * A209434 A209435 A209436

Keyword

nonn,hard,fini,more

Author

François Labelle, Mar 08 2012

Extensions

a(11) from François Labelle, Feb 27 2017

Status

approved