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A290721
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a(n) = 4^n - n - 1.
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0
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2, 13, 60, 251, 1018, 4089, 16376, 65527, 262134, 1048565, 4194292, 16777203, 67108850, 268435441, 1073741808, 4294967279, 17179869166, 68719476717, 274877906924, 1099511627755, 4398046511082, 17592186044393, 70368744177640, 281474976710631, 1125899906842598
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OFFSET
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1,1
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COMMENTS
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For n > 1, also the number of (non-null) connected induced subgraphs in the n-cocktail party graph.
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LINKS
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FORMULA
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a(n) = 4^n - n - 1.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
G.f.: ((-2 - x) x)/((-1 + x)^2 (-1 + 4 x)).
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MATHEMATICA
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Table[4^n - n - 1, {n, 20}]
LinearRecurrence[{6, -9, 4}, {2, 13, 60}, 20]
CoefficientList[Series[(-2 - x)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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