A360387 - OEIS

%I #93 Mar 04 2023 02:09:33

%S 1,1,2,2,2,3,1,3,1,3,1,2,2,4,2,2,4,3,1,4,3,1,6,1,1,3,1,4,4,1,1,1,1,5,

%T 1,2,5,1,1,1,3,1,1,1,2,6,1,1,2,1,1,3,1,4,1,2,1,5,1,1,1,5,1,1,1,3,1,2,

%U 2,7,1,2,2,3,1,6,1,1,4,2,2,4,3,1,3,1,2

%N a(1) = 1, and for n > 1, a(n) is the number of ways that a(1..n-1) can be divided into contiguous subsequences of equal sum.

%C No divisions counts as 1 way of dividing the sequence.

%C Is the sequence unbounded?

%H Samuel Harkness, <a href="/A360387/b360387.txt">Table of n, a(n) for n = 1..10000</a>

%e Initial terms with corresponding divisions (starting with single subsequence, then more):

%e  n  a(n)  Ways of dividing (subsequences separated by "|")

%e  -  ----  ------------------------------------------------

%e  1     1

%e  2     1  [1]

%e  3     2  [1,1]; [1|1]

%e  4     2  [1,1,2]; [1,1|2]

%e  5     2  [1,1,2,2]; [1,1|2|2]

%e  6     3  [1,1,2,2,2]; [1,1,2|2,2]; [1,1|2|2|2]

%e  7     1  [1,1,2,2,2,3]

%e  8     3  [1,1,2,2,2,3,1]; [1,1,2,2|2,3,1]; [1,1,2|2,2|3,1]

%e  9     1  [1,1,2,2,2,3,1,3]

%e 10     3  [1,1,2,2,2,3,1,3,1]; [1,1,2,2,2|3,1,3,1]; [1,1,2|2,2|3,1|3,1]

%o (PARI) { m = s = 0; v = 1; for (n=1, 87, print1 (v", "); m += 2^s+=v; v = 0; fordiv (s, d, t = sum(i=1, d, 2^(i*s/d)); if (bitand(m, t)==t, v++))) } \\ _Rémy Sigrist_, Feb 09 2023

%Y Cf. A308746.

%K nonn

%O 1,3

%A _Neal Gersh Tolunsky_, Feb 05 2023