cp's OEIS Frontend

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 A372595 #10 May 08 2024 14:56:42
%S A372595 0,1,2,3,3,4,5,13,37,4,5,6,14,38,7,9,37,22539988369405
%N 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).
%C A372595 T(4,9) = 41*2^39 - 3 = 22539988369405.
%C A372595 T(4,10) = (97*2^95+1)*2^(97*2^95-1) - 3 (1156727590779508264240712695467 digits).
%F A372595 T(n,k) = T(n-1,k)+1 if 1 <= k <= A000108(n-1).
%e A372595 Triangle begins:
%e A372595   0;
%e A372595   1;
%e A372595   2, 3;
%e A372595   3, 4, 5, 13, 37;
%e A372595   4, 5, 6, 14, 38, 7, 9, 37, 22539988369405, ...;
%e A372595   ...
%Y A372595 Last elements on each row give A372478.
%Y A372595 Cf. A000108, A063171, A372592, A372593, A372594.
%K A372595 nonn,tabf
%O A372595 0,3
%A A372595 _Pontus von Brömssen_, May 06 2024