A372595 - OEIS

A372595

Irregular triangle read by rows, where the n-th row gives the number of steps in the hydra game (the version described in A372478) when the initial hydra is each of the A000108(n) ordered trees with n edges (ordered by lexicographic order of their corresponding Dyck words as in A063171).

%I #10 May 08 2024 14:56:42

%S 0,1,2,3,3,4,5,13,37,4,5,6,14,38,7,9,37,22539988369405

%N Irregular triangle read by rows, where the n-th row gives the number of steps in the hydra game (the version described in A372478) when the initial hydra is each of the A000108(n) ordered trees with n edges (ordered by lexicographic order of their corresponding Dyck words as in A063171).

%C T(4,9) = 41*2^39 - 3 = 22539988369405.

%C T(4,10) = (97*2^95+1)*2^(97*2^95-1) - 3 (1156727590779508264240712695467 digits).

%F T(n,k) = T(n-1,k)+1 if 1 <= k <= A000108(n-1).

%e Triangle begins:

%e 0;

%e 1;

%e 2, 3;

%e 3, 4, 5, 13, 37;

%e 4, 5, 6, 14, 38, 7, 9, 37, 22539988369405, ...;

%e ...

%Y Last elements on each row give A372478.

%Y Cf. A000108, A063171, A372592, A372593, A372594.

%K nonn,tabf

%O 0,3

%A _Pontus von Brömssen_, May 06 2024