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A325538
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Number of subsets of {1..n} whose product is one more than the sum of their complement.
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2
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1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 4, 2, 2, 4, 2, 2, 5, 5, 1, 2, 2, 3, 2, 5, 3, 4, 2, 2, 3, 10, 2, 4, 7, 5, 3, 3, 7, 6, 4, 4, 5, 5, 5, 2, 6, 4, 6, 5, 3, 8, 4, 5, 4, 5, 2, 10, 5, 3, 7, 11, 6, 10, 5, 11, 6, 4, 7, 6, 10
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OFFSET
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0,13
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COMMENTS
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Also by definition the number of subsets whose sum is one fewer than the product of their complement.
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LINKS
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EXAMPLE
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The initial terms count the following subsets:
0: {}
1: {1}
2: {2}
3: {1,3}
4: {2,3}
7: {4,5}
10: {1,6,7}
12: {7,9}
12: {1,2,4,8}
14: {2,5,9}
14: {1,2,4,11}
15: {1,3,5,7}
16: {3,4,10}
16: {1,3,5,8}
17: {1,10,13}
18: {2,5,15}
19: {11,15}
19: {1,2,6,14}
20: {1,4,6,8}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], 1+Plus@@#==Times@@Complement[Range[n], #]&]], {n, 0, 10}]
ric[n_, pr_, s_, lst_, t_] := Block[{k}, If[pr == t-s, cnt++]; Do[ If[pr k <= t, ric[n, pr k, s + k, k, t], Break[]], {k, lst+1, n}]]; a[n_] := (cnt = 0; ric[n, 1, 0, 0, n (n + 1)/2 + 1]; cnt); a /@ Range[0, 85] (* Giovanni Resta, Sep 13 2019 *)
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CROSSREFS
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Cf. A028422, A053632, A059529, A063865, A178830, A301987, A325041, A326172, A326173, A326174, A326175, A326179, A326180, A326441.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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