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A328890
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Number of acyclic edge covers of the complete bipartite graph K_{n,2}.
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2
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1, 6, 18, 46, 110, 254, 574, 1278, 2814, 6142, 13310, 28670, 61438, 131070, 278526, 589822, 1245182, 2621438, 5505022, 11534334, 24117246, 50331646, 104857598, 218103806, 452984830, 939524094, 1946157054, 4026531838, 8321499134, 17179869182, 35433480190, 73014444030
(list;
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history;
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internal format)
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OFFSET
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1,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).
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FORMULA
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a(n) = 2*A000225(n-1) + A001787(n).
a(n) = (2 + n)*2^(n-1) - 2.
From Colin Barker, Nov 05 2019: (Start)
G.f.: x*(1 + x - 4*x^2) / ((1 - x)*(1 - 2*x)^2).
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>3.
(End)
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PROG
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(PARI) a(n) = {(2 + n)*2^(n-1) - 2}
(PARI) Vec(x*(1 + x - 4*x^2) / ((1 - x)*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Nov 05 2019
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CROSSREFS
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Column 2 of A328888.
Cf. A000225, A001787.
Sequence in context: A031128 A304161 A261016 * A188379 A299268 A248462
Adjacent sequences: A328887 A328888 A328889 * A328891 A328892 A328893
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KEYWORD
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nonn,easy
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AUTHOR
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Andrew Howroyd, Oct 29 2019
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STATUS
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approved
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