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A357602 a(n) is the number of n-gons in A000940 that are asymmetric.

0, 0, 0, 1, 15, 121, 1026, 8696, 81515, 827282, 9200052

Offset: 3

Ian Mooney, Oct 05 2022

			Of the A000940(6) = 12 hexagons, 11 have symmetry and 1 is asymmetric, so a(6)=1.

Cf. A000940, A342533.

a(n) = A000940(n) - A342533(n).

a(p) = ((((p-1)! + 1)/p) + p - 2 - (2^((p-1)/2)*((p-1)/2)!))/4 for prime p. See A007619.

A342533 a(n) is the number of n-gons in A000940 that display symmetry (reflection / rotation).

Original entry on oeis.org

1, 2, 4, 11, 24, 81, 193, 772, 1920, 8735, 23040

Offset: 3

Ian Mooney, Mar 14 2021

			Of the A000940(6)=12 hexagons, 11 have symmetry and 1 is asymmetric, so a(6)=11.

Cf. A000940.

a(p) = (2^((p-1)/2)*((p-1)/2)!)/2 for prime p.

A066646 Arrange the permutations of {1..m} in lexicographic order. Sequence gives indices of permutations of orders 1 or 2.

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 15, 17, 22, 24, 25, 26, 27, 30, 55, 56, 61, 68, 81, 83, 87, 95, 106, 108, 112, 120, 121, 122, 123, 126, 127, 128, 135, 137, 142, 144, 265, 266, 267, 270, 289, 290, 315, 317, 340, 342, 391, 392, 397, 404, 415, 416, 445, 451, 470, 476, 513, 515

Offset: 1

Ian Mooney, Jan 09 2002

Independent of choice of m as long as m! exceeds index.

			Take m=4, say. The first few permutations are 1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, ... and numbers 1,2,3,6,7,8,... have orders 1 or 2. This gives the first 6 terms.

A067897 a(n) = A000085(n) - (1 + Sum_{j=1..n-1} A000085(j)).

Original entry on oeis.org

0, 0, 0, 0, 2, 8, 32, 112, 412, 1504, 5760, 22464, 91224, 379424, 1632896, 7201472, 32709136, 152094976, 725810176, 3540883968, 17680145184, 90115509888, 469094763008, 2489169367808, 13465672180160, 74161734785536

Offset: 0

Ian Mooney, May 15 2003

nonn

			a(5) = A000085(5) - (1 + Sum_{j=1..4} A000085(j)) = 26 - (1 + 1 + 2 + 4 + 10) = 26 - 18 = 8. - _Jon E. Schoenfield_, Mar 14 2021

Cf. A000085, A245176.

a(n) = A000085(n) - A245176(n-1). - Jon E. Schoenfield, Mar 14 2021

Missing initial 0 term added by Jon E. Schoenfield, Mar 16 2021

cp's OEIS Frontend

User: Ian Mooney

A357602 a(n) is the number of n-gons in A000940 that are asymmetric.

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A342533 a(n) is the number of n-gons in A000940 that display symmetry (reflection / rotation).

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Author

Keywords

Examples

Crossrefs

Formula

A066646 Arrange the permutations of {1..m} in lexicographic order. Sequence gives indices of permutations of orders 1 or 2.

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Author

Keywords

Comments

Examples

A067897 a(n) = A000085(n) - (1 + Sum_{j=1..n-1} A000085(j)).

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Author

Keywords

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