A285878 Number of possible chess games at the end of the n-th ply starting with just pawns and king.

1, 18, 324, 5658, 98766, 1683597, 28677387, 479763588, 8014917042, 132060434889, 2170519816231

Offset

0,2

Comments

Gives the number of possible chess games where both sides start without queens, rooks, knights, and bishops.

Does not include games which end in fewer than n plies.

Initial terms computed using the Chesspresso engine.

Links

Table of n, a(n) for n=0..10.

Bernhard Seybold, Chesspresso.

Example

a(1) = 18 since each pawn can move forward 1 or 2 squares (16 moves) or the king can move left or right (2 moves).

Crossrefs

Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns).

Sequence in context: A207465 A207240 A207498 * A171292 A001027 A285875

Adjacent sequences: A285875 A285876 A285877 * A285879 A285880 A285881

Keyword

nonn,hard,more,fini

Author

Sean A. Irvine, Apr 28 2017

Extensions

a(10) from Sean A. Irvine, May 04 2017

Status

approved