A378902 a(n) is the number of paths of a chess king on square a1 to reach a position outside an 8 X 8 chessboard after n steps.

5, 6, 39, 156, 922, 5060, 31165, 196605, 1301490, 8844147, 61504902, 434181564, 3098427480, 22270496859, 160854381441

Offset

1,1

Comments

The king visits the Moore neighborhood, and the 8 possible moves relative to its current position are E, NE, N, NW, W, SW, S, and SE.

Links

Table of n, a(n) for n=1..15.

Example

a(1) = 5: only the 3 moves E, NE, and N end on target squares on the chessboard, the other 5 leave the board.
a(2) = 6: the 6 combinations of step directions leaving the board in exactly 2 moves are [E,SW], [E,S], [E,SE], [N,NE], [N,E], and [N,SE].

Crossrefs

Cf. A140518, A376609, A376610, A377018.

Sequence in context: A333218 A349051 A137254 * A262308 A355137 A352641

Adjacent sequences: A378899 A378900 A378901 * A378903 A378909 A378910

Keyword

nonn,walk,more,new

Author

Hugo Pfoertner, Dec 10 2024

Status

approved