A056207 Number of binary trees of height <= n.

3, 24, 675, 458328, 210066388899, 44127887745906175987800, 1947270476915296449559703445493848930452791203, 3791862310265926082868235028027893277370233152247388584761734150717768254410341175325352024

Offset

1,1

References

Todd K. Moon, "Enumerations of binary trees, types of trees and the number of reversible variable length codes," submitted to Discrete Applied Mathematics, 2000.

Links

Table of n, a(n) for n=1..8.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Formula

a(n) = d(n) + a(n-1), d(n) = A001699(n) is the number of binary trees of depth exactly n.

a(n) = A003095(n+2) - 2 = A004019(n+1) - 1 = a(n-1)^2 + 4*a(n-1) + 3.

Prog

(Python)
from itertools import accumulate
def f(anm1, _): return anm1**2 + 4*anm1 + 3
def aupton(terms): return list(accumulate([3]*terms, f))
print(aupton(8)) # Michael S. Branicky, Mar 24 2021

Crossrefs

Cf. A001699, A002449, A003095.

Sequence in context: A292813 A293249 A202944 * A297561 A326084 A301525

Adjacent sequences: A056204 A056205 A056206 * A056208 A056209 A056210

Keyword

easy,nonn

Author

Todd K. Moon (Todd.Moon(AT)ece.usu.edu), Aug 02 2000

Extensions

More terms from Henry Bottomley, Jul 09 2001

Status

approved