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A285387 Number of ordered (n+1)-tuples of positive integers (s_1, s_2, ..., s_{n+1}) with s_(n+1) - s_n - ... - s_1 = s_(n+1)/(s_n * ... * s_1). 0

%I #14 May 04 2017 00:21:47

%S 1,3,3,7,3,6,6,6,5,9,5,12,6,6,6,11,7,12,6,11

%N Number of ordered (n+1)-tuples of positive integers (s_1, s_2, ..., s_{n+1}) with s_(n+1) - s_n - ... - s_1 = s_(n+1)/(s_n * ... * s_1).

%C a(n) >= 3 for n > 1: (1, ..., 1, 2, 2*(n+1)); (1, ..., 1, (n+1), 2*(n+1)) and (1, ..., 1, 2, n+1, 2*(n+1)) are always solutions.

%e For n=2, there are 3 solutions:

%e (1, 2, 6) is a solution since 6 / (2 * 1) = 3 = 6 - 2 - 1;

%e (1, 3, 6) is a solution since 6 / (3 * 1) = 2 = 6 - 3 - 1;

%e (2, 3, 6) is a solution since 6 / (3 * 2) = 1 = 6 - 3 - 2.

%K nonn,more

%O 1,2

%A _Reiner Moewald_, Apr 18 2017

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