A378235 Number of winning positions of Gordon Hamilton's Jumping Frogs game with single frogs, where the distance between the leftmost frog and the rightmost frog is equal to n.

1, 1, 1, 3, 4, 7, 13, 23, 40, 74, 148, 263, 493, 934, 1719, 3192, 6035, 11280, 21252, 40367, 75796

Offset: 0

Author

Pontus von Brömssen, Nov 20 2024

Keywords

• nonn
• more

Comments

For the rules of the Jumping Frogs game, see A377232.

A winning position and its reversal are both counted.

a(n) is the number of terms x of A377232 in the interval 2^n <= x < 2^(n+1).

Examples

			For n = 0, the only winning position is 1, so a(0) = 1.
For n = 1, the only winning position is 11, so a(1) = 1.
For n = 2, the only winning position is 111, so a(2) = 1.
For n = 3, there are a(3) = 3 winning positions: 1011, 1101, 1111.
For n = 4, there are a(4) = 4 winning positions: 10111, 11011, 11101, 11111.
For n = 5, there are a(5) = 7 winning positions: 100111, 101111, 110111, 111001, 111011, 111101, 111111.
		

Crossrefs

Cf. A377232, A378004.