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

0,4

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).

Links

Table of n, a(n) for n=0..20.

Example

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.

Sequence in context: A299024 A116201 A280224 * A282718 A092406 A250297

Adjacent sequences: A378232 A378233 A378234 * A378236 A378237 A378238

Keyword

nonn,more

Author

Pontus von Brömssen, Nov 20 2024

Status

approved