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A071539
Number of n-tuples of elements e_1,e_2,...,e_n in the symmetric group S_3 such that the subgroup generated by e_1,e_2,...,e_n is S_3.
1
0, 18, 168, 1170, 7440, 45738, 277368, 1672290, 10056480, 60404058, 362613768, 2176238610, 13059075120, 78359331978, 470170537368, 2821066664130, 16926529911360, 101559568461498, 609358576176168, 3656154950132850, 21936940173733200, 131621672448624618, 789730128885258168
OFFSET
1,2
FORMULA
a(n) = 6^n - 3*2^n - 3^n + 3.
G.f.: 6*x^2*(3 - 8*x) / (1 - 12*x + 47*x^2 - 72*x^3 + 36*x^4). [Corrected by Georg Fischer, May 15 2019]
MATHEMATICA
LinearRecurrence[{12, -47, 72, -36}, {0, 18, 168, 1170, 7440}, 23] (* Georg Fischer, May 15 2019 *)
PROG
(PARI) a(n) = 6^n - 3*2^n - 3^n + 3; \\ Michel Marcus, Oct 31 2017
CROSSREFS
Sequence in context: A055915 A208827 A327792 * A125381 A126539 A213802
KEYWORD
nonn,easy
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Jun 02 2002
EXTENSIONS
More terms from Michel Marcus, Oct 31 2017
STATUS
approved