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).

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

Offset: 0

Author

Pontus von Brömssen, May 06 2024

Keywords

• nonn
• tabf

Comments

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

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

Examples

			Triangle begins:
  0;
  1;
  2, 3;
  3, 4, 5, 13, 37;
  4, 5, 6, 14, 38, 7, 9, 37, 22539988369405, ...;
  ...
		

Crossrefs

Last elements on each row give A372478.

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

Formula

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