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

0,3

Comments

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

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

Links

Table of n, a(n) for n=0..17.

Formula

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

Example

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.

Sequence in context: A157725 A372592 A238394 * A182503 A278288 A023154

Adjacent sequences: A372592 A372593 A372594 * A372596 A372597 A372598

Keyword

nonn,tabf

Author

Pontus von Brömssen, May 06 2024

Status

approved