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A192033
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Expansion of x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).
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2
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0, 1, 3, 10, 21, 46, 93, 190, 381, 766, 1533, 3070, 6141, 12286, 24573, 49150, 98301, 196606, 393213, 786430, 1572861, 3145726, 6291453, 12582910, 25165821, 50331646, 100663293, 201326590, 402653181, 805306366, 1610612733, 3221225470, 6442450941, 12884901886
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of edges of the shuffle-exchange graph SE_n with self-loops removed.
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LINKS
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FORMULA
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G.f.: x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).
a(n) = 3*2^(n-1) -3 + (n mod 2) for n>0, a(0) = 0.
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MAPLE
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a:= n-> `if`(n=0, 0, 3*2^(n-1) -3 +irem(n, 2)):
seq(a(n), n=0..40);
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MATHEMATICA
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LinearRecurrence[{2, 1, -2}, {0, 1, 3, 10}, 40] (* Harvey P. Dale, Mar 23 2018 *)
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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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