A020902 Number of nonisomorphic cyclic subgroups of alternating group A_n (or number of distinct orders of even permutations of n objects); number of different LCM's of partitions of n which have even number of even parts.

1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 18, 22, 26, 30, 35, 39, 46, 51, 60, 67, 76, 84, 94, 105, 119, 133, 147, 162, 176, 196, 218, 240, 263, 286, 310, 340, 374, 409, 441, 476, 515, 559, 608, 662, 711, 762, 817, 883, 955, 1030, 1104, 1177, 1257, 1352, 1453, 1559

Offset

0,4

References

V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

Links

Table of n, a(n) for n=0..57.

Formula

a(n) = A009490(n-2) + A035942(n-1) + A035942(n), n > 1, a(0)=a(1)=1.

Example

a(8)=8 because lcm{1^8} = 1, lcm{1^4 * 2^2, 2^4} = 2, lcm{1^5 * 3^1, 1^2 * 3^2} = 3, lcm{4^2, 1^2 * 2^1 * 4^1} = 4, lcm{1^3 * 5^1} = 5, lcm{2^1 * 6^1, 1^1 * 2^2 * 3^1} = 6, lcm{1^1 * 7^1} = 7, lcm{3^1 * 5^1} = 15.

Crossrefs

Cf. A034891.

Sequence in context: A176176 A174090 A280083 * A008751 A029002 A280241

Adjacent sequences: A020899 A020900 A020901 * A020903 A020904 A020905

Keyword

nonn

Author

Vladeta Jovovic

Status

approved