A378235 - OEIS

%I #9 Nov 21 2024 05:22:31

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

%T 40367,75796

%N 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.

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

%C A winning position and its reversal are both counted.

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

%e For n = 0, the only winning position is 1, so a(0) = 1.

%e For n = 1, the only winning position is 11, so a(1) = 1.

%e For n = 2, the only winning position is 111, so a(2) = 1.

%e For n = 3, there are a(3) = 3 winning positions: 1011, 1101, 1111.

%e For n = 4, there are a(4) = 4 winning positions: 10111, 11011, 11101, 11111.

%e For n = 5, there are a(5) = 7 winning positions: 100111, 101111, 110111, 111001, 111011, 111101, 111111.

%Y Cf. A377232, A378004.

%K nonn,more

%O 0,4

%A _Pontus von Brömssen_, Nov 20 2024