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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.
2
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V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.
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
KEYWORD
nonn
STATUS
approved