Calculate the number of trees in which Fitch parsimony will reconstruct
*m* steps, where *a* leaves are labelled with one state, and *b* leaves are
labelled with a second state.

```
Carter1(m, a, b)
Log2Carter1(m, a, b)
LogCarter1(m, a, b)
```

- m
Number of steps.

- a, b
Number of leaves labelled

`0`

and`1`

.

Implementation of theorem 1 from Carter et al. (1990)

Carter M, Hendy M, Penny D, Székely LA, Wormald NC (1990).
“On the distribution of lengths of evolutionary trees.”
*SIAM Journal on Discrete Mathematics*, **3**(1), 38--47.
doi:10.1137/0403005
.

See also:

Steel MA (1993).
“Distributions on bicoloured binary trees arising from the principle of parsimony.”
*Discrete Applied Mathematics*, **41**(3), 245--261.
doi:10.1016/0166-218X(90)90058-K
.

Steel M, Charleston M (1995).
“Five surprising properties of parsimoniously colored trees.”
*Bulletin of Mathematical Biology*, **57**(2), 367--375.
doi:10.1016/0092-8240(94)00051-D
.

(Steel M, Goldstein L, Waterman MS (1996).
“A central limit theorem for the parsimony length of trees.”
*Advances in Applied Probability*, **28**(4), 1051--1071.
doi:10.2307/1428164
.
)

Other profile parsimony functions:
`PrepareDataProfile()`

,
`StepInformation()`

,
`WithOneExtraStep()`

,
`profiles`

```
# The character `0 0 0 1 1 1`
Carter1(1, 3, 3) # Exactly one step
#> [1] 9
Carter1(2, 3, 3) # Two steps (one extra step)
#> [1] 54
# Number of trees that the character can map onto with exactly _m_ steps
# if non-parsimonious reconstructions are permitted:
cumsum(sapply(1:3, Carter1, 3, 3))
#> [1] 9 63 105
# Three steps allow the character to map onto any of the 105 six-leaf trees.
```