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A071765
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Number of n-tuples of elements e_1,e_2,...,e_n in the alternating group A_4 such that the subgroup generated by e_1,e_2,...,e_n is A_4.
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1
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0, 96, 1560, 20160, 246840, 2978976, 35806680, 429889920, 5159439480, 61916079456, 743003467800, 8916081545280, 106993131892920, 1283918176981536, 15407020443448920, 184884254427882240, 2218611089044007160, 26623333210616085216, 319479999091095974040
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: (-360x^2 + 96x) / (-144x^4 + 240x^3 - 115x^2 + 20x - 1).
G.f.: 24*x*(4 - 15*x)/((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 12*x)). - Andrew Howroyd, Jul 04 2018
a(n) = 20*a(n-1) - 115*a(n-2) + 240*a(n-3) - 144*a(n-4). - Vincenzo Librandi, Jul 04 2018
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MATHEMATICA
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LinearRecurrence[{20, -115, 240, -144}, {0, 96, 1560, 20160}, 40] (* Vincenzo Librandi, Jul 04 2018 *)
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PROG
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(PARI) concat([0], Vec(24*(4 - 15*x)/((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 12*x)) + O(x^20))) \\ Andrew Howroyd, Jul 04 2018
(Magma) I:=[0, 96, 1560, 20160]; [n le 4 select I[n] else 20*Self(n-1)- 115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 04 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), Jun 04 2002
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EXTENSIONS
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STATUS
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approved
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