Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000416
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Mapping
St000416: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
 => 1
[[],[]]
 => 1
[[[]]]
 => 1
[[],[],[]]
 => 1
[[],[[]]]
 => 3
[[[]],[]]
 => 3
[[[],[]]]
 => 1
[[[[]]]]
 => 1
[[],[],[],[]]
 => 1
[[],[],[[]]]
 => 6
[[],[[]],[]]
 => 6
[[],[[],[]]]
 => 4
[[],[[[]]]]
 => 4
[[[]],[],[]]
 => 6
[[[]],[[]]]
 => 3
[[[],[]],[]]
 => 4
[[[[]]],[]]
 => 4
[[[],[],[]]]
 => 1
[[[],[[]]]]
 => 3
[[[[]],[]]]
 => 3
[[[[],[]]]]
 => 1
[[[[[]]]]]
 => 1
[[],[],[],[],[]]
 => 1
[[],[],[],[[]]]
 => 10
[[],[],[[]],[]]
 => 10
[[],[],[[],[]]]
 => 10
[[],[],[[[]]]]
 => 10
[[],[[]],[],[]]
 => 10
[[],[[]],[[]]]
 => 15
[[],[[],[]],[]]
 => 10
[[],[[[]]],[]]
 => 10
[[],[[],[],[]]]
 => 5
[[],[[],[[]]]]
 => 15
[[],[[[]],[]]]
 => 15
[[],[[[],[]]]]
 => 5
[[],[[[[]]]]]
 => 5
[[[]],[],[],[]]
 => 10
[[[]],[],[[]]]
 => 15
[[[]],[[]],[]]
 => 15
[[[]],[[],[]]]
 => 10
[[[]],[[[]]]]
 => 10
[[[],[]],[],[]]
 => 10
[[[[]]],[],[]]
 => 10
[[[],[]],[[]]]
 => 10
[[[[]]],[[]]]
 => 10
[[[],[],[]],[]]
 => 5
[[[],[[]]],[]]
 => 15
[[[[]],[]],[]]
 => 15
[[[[],[]]],[]]
 => 5
[[[[[]]]],[]]
 => 5
Description
The number of inequivalent increasing trees of an ordered tree. The total number of increasing trees is [[St000085]].