A245079 -id:A245079 - cp's OEIS frontend

A305000 Number of labeled antichains of finite sets spanning some subset of {1,...,n} with singleton edges allowed.

1, 2, 8, 72, 1824, 220608, 498243968, 309072306743552, 14369391925598802012151296, 146629927766168786239127150948525247729660416

Offset: 0

Gus Wiseman, May 23 2018

Only the non-singleton edges are required to form an antichain.

Number of non-degenerate unate Boolean functions of n or fewer variables. - Aniruddha Biswas, May 11 2024

			The a(2) = 8 antichains:
  {}
  {{1}}
  {{2}}
  {{1,2}}
  {{1},{2}}
  {{1},{1,2}}
  {{2},{1,2}}
  {{1},{2},{1,2}}

Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 12.
Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Cf. A006126, A261005, A304996, A304997, A304998, A304999, A305000, A305001.
Cf. A000372, A003182, A014466, A293606, A293993, A306505, A320449, A321679.
Cf. A245079.

Binomial transform of A304999.

Inverse binomial transform of A245079. - Aniruddha Biswas, May 11 2024

a(5)-a(8) from Gus Wiseman, May 31 2018

a(9) from Aniruddha Biswas, May 11 2024

A372495 Number of inequivalent unate functions of n or fewer variables.

Original entry on oeis.org

2, 4, 10, 34, 200, 3466, 829744

Offset: 0

Aniruddha Biswas, May 03 2024

A Boolean function is unate in a variable if it is either nondecreasing or nonincreasing with respect to that variable. Therefore in the circuit representation of unate functions, each variable appears either in its original form or in complemented form. Thus x⊕y = (x∧¬y)∨(¬x∧y) is not a unate function.

Moreover, two Boolean functions are said to be equivalent if they are equivalent under the permutation of variables. For example, f(x,y)=x is equivalent to f(x,y)=y under the permutation of input variables.

			The list of all 2-variable inequivalent unate functions f(x,y) is 0,1,x,¬x,x∧y,¬x∧y,¬x∧¬y,x∨y,¬x∨y,¬x∨¬y. So a(2)=10.

Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 16.
Index entries for sequences related to Boolean functions

Cf. A000372, A003182, A245079.

A373697 Number of nondegenerate balanced unate functions of n or fewer variables.

Original entry on oeis.org

0, 2, 0, 8, 256, 16832, 31287424, 10393552784640

Offset: 0

Aniruddha Biswas, Jun 13 2024

Aniruddha Biswas and P. Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 13.
Index entries for sequences related to Boolean functions

Cf. A006126, A006602, A341633, A245079.

A374399 Number of inequivalent nondegenerate unate functions of n or fewer variables.

Original entry on oeis.org

2, 2, 6, 24, 166, 3266, 826308

Offset: 0

Aniruddha Biswas, Jul 07 2024

A Boolean function is degenerate on some variable if its output does not depend on the variable, and it is said to be non-degenerate if it is not degenerate on any variable.

Appears to be (essentially) the partial sums of A304997. - N. J. A. Sloane, Jul 26 2024

Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 16.
Index entries for sequences related to Boolean functions

Cf. A373697, A372495, A000372, A003182, A245079.

A373690 Number of balanced unate functions of n or fewer variables.

Original entry on oeis.org

0, 2, 4, 14, 296, 18202, 31392428, 10393772159334

Offset: 0

Aniruddha Biswas, Jun 13 2024

Aniruddha Biswas and P. Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 13.
Index entries for sequences related to Boolean functions

Cf. A341633, A245079.

Typo in a(3) corrected by Andrei Zabolotskii, Jul 29 2025

A374400 Number of balanced inequivalent unate functions of n or fewer variables.

Original entry on oeis.org

0, 2, 2, 6, 24, 254, 50172

Offset: 0

Aniruddha Biswas, Jul 07 2024

A Boolean function is said to be balanced if it takes the values 0 and 1 an equal number of times.

Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 16.
Index entries for sequences related to Boolean functions

Cf. A341633, A245079, A003182, A000372, A372495, A000721.

A374401 Number of balanced inequivalent nondegenerate unate functions of n or fewer variables.

Original entry on oeis.org

0, 2, 0, 4, 18, 230, 49918

Offset: 0

Aniruddha Biswas, Jul 07 2024

Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 16.
Index entries for sequences related to Boolean functions

Cf. A341633, A245079, A003182, A000372, A372495, A373697, A000721.

cp's OEIS Frontend

A305000 Number of labeled antichains of finite sets spanning some subset of {1,...,n} with singleton edges allowed.

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A372495 Number of inequivalent unate functions of n or fewer variables.

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A373697 Number of nondegenerate balanced unate functions of n or fewer variables.

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A374399 Number of inequivalent nondegenerate unate functions of n or fewer variables.

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A373690 Number of balanced unate functions of n or fewer variables.

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A374400 Number of balanced inequivalent unate functions of n or fewer variables.

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A374401 Number of balanced inequivalent nondegenerate unate functions of n or fewer variables.

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