cp's OEIS Frontend

A360387 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.

%I A360387 #93 Mar 04 2023 02:09:33
%S A360387 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 A360387 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 A360387 2,7,1,2,2,3,1,6,1,1,4,2,2,4,3,1,3,1,2
%N A360387 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 A360387 No divisions counts as 1 way of dividing the sequence.
%C A360387 Is the sequence unbounded?
%H A360387 Samuel Harkness, <a href="/A360387/b360387.txt">Table of n, a(n) for n = 1..10000</a>
%e A360387 Initial terms with corresponding divisions (starting with single subsequence, then more):
%e A360387  n  a(n)  Ways of dividing (subsequences separated by "|")
%e A360387  -  ----  ------------------------------------------------
%e A360387  1     1
%e A360387  2     1  [1]
%e A360387  3     2  [1,1]; [1|1]
%e A360387  4     2  [1,1,2]; [1,1|2]
%e A360387  5     2  [1,1,2,2]; [1,1|2|2]
%e A360387  6     3  [1,1,2,2,2]; [1,1,2|2,2]; [1,1|2|2|2]
%e A360387  7     1  [1,1,2,2,2,3]
%e A360387  8     3  [1,1,2,2,2,3,1]; [1,1,2,2|2,3,1]; [1,1,2|2,2|3,1]
%e A360387  9     1  [1,1,2,2,2,3,1,3]
%e A360387 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 A360387 (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 A360387 Cf. A308746.
%K A360387 nonn
%O A360387 1,3
%A A360387 _Neal Gersh Tolunsky_, Feb 05 2023