stack size info

[A Soare]

16.7 Byte-Code Function Objects
===============================

STACKSIZE
     The maximum stack size this function needs.

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(defun p (n)
  "sum"
  (if (> n 1) (+ n (p (1- n)))
    n))



(byte-compile 'p)
(symbol-function 'p)

#[(n)
  "..."
  [n 1 p]
  3            <=<= here is the stack size.
  "sum"]

But I believe that a recursive function has the stack greater, 3*n, not 3. For 
every recursion I believe that the stack size get greater with 3, so the stack 
is dependent of n. Is it true?

Is this a little error of explanation in INFO file?