If a is the smallest element of such a set, then 15 - a is the largest element, and
for the remaining elements we may choose any (or none) of the 14 - 2a elements:
a + 1; a + 2; ... ; (13- a) - 1.

Thus there are 2^(14-2a) sets whose smallest element
is a.
Since (15-a)>a causes a < 8, the summation of 2^(14-2a) over l a = 1; 2; ...; 7 provides an answer: 2^12*2^10+2^8+2^6+2^4+2^2+2^0 =4096+1024+256+64+16+4+1=5461

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