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 A292729 a(n) is the maximum number of steps that can occur during the following procedure: start with n piles each containing one stone; any number of stones can be transferred between piles of equal size. 2
 0, 1, 1, 3, 4, 4, 8, 10, 11, 12, 16, 20, 22, 24, 27, 31, 35, 38, 43, 45, 47, 52, 57, 62, 67, 71, 74, 79, 83, 90, 95, 101, 106, 111, 114, 118, 126, 132, 138, 146, 152, 156, 161, 167, 172, 180, 189, 194, 204, 208, 216, 221, 228, 234, 242, 249, 258, 264, 274, 282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Note that more than one stone can be moved during a single move. A121924 is the analogous sequence if only one stone can be transferred between piles of equal size. A011371 is the analogous sequence if all stones must be transferred between piles of equal size (i.e., the number of stones in each pile must be a power of two). Both A121924 and A011371 are lower bounds for this sequence. LINKS EXAMPLE For n = 7, an 8-move sequence is: (1 1 1 1 1 1 1) -> (2 1 1 1 1 1) -> (2 2 1 1 1) -> (3 1 1 1 1) -> (3 2 1 1) -> (3 2 2) -> (3 3 1) -> (5, 1, 1) -> (5 2). PROG (Python) def A292729(n): ....s_in = set([(1, )*n]) ....count=-1 ....while len(s_in) > 0: ........s_out = set() ........for s in s_in: ............last = -1 ; idx = 0 ............while (idx+1) < len(s): ................h = s[idx] ................if h!=last and s[idx+1]==h: ....................for q in range(1, h+1): ........................lst = list(s[:idx]) + list(s[idx+2:]) ........................lst += [2*h] if h==q else [ h-q, h+q] ........................t = tuple(sorted(lst)) ........................if not t in s_out: ............................s_out.add(t) ................last = s[idx] ; idx += 1 ........count += 1 ........s_in = s_out ....return count # Bert Dobbelaere, Jul 14 2019 CROSSREFS Cf. A011371, A121924, A292726, A292728. Sequence in context: A127735 A330249 A075550 * A328989 A137529 A245258 Adjacent sequences:  A292726 A292727 A292728 * A292730 A292731 A292732 KEYWORD nonn AUTHOR Peter Kagey, Sep 22 2017 EXTENSIONS a(35)-a(60) from Bert Dobbelaere, Jul 14 2019 STATUS approved

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Last modified August 9 13:57 EDT 2020. Contains 336323 sequences. (Running on oeis4.)