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A339891
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Number of fundamentally different graceful labelings of the complete tripartite graph K_1,1,n.
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2
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1, 4, 7, 12, 20, 34, 74, 131, 260, 524, 1030, 2054, 4118, 8196, 16389, 32804, 65554, 131074, 262216, 524292, 1048580, 2097304, 4194312, 8388619, 16777478, 33554436, 67108906, 134218244, 268435464, 536870914, 1073742880, 2147483720, 4294967300, 8589936646, 17179869193
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OFFSET
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1,2
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COMMENTS
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The difference between "fundamentally different graceful labelings" of a graph and "graceful labelings" of a graph is that the latter is the former multiplied by twice the number of automorphisms. (The extra factor of 2 comes from complementation.)
When n>1, the graph K_1,1,n has 2n! automorphisms.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation.
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LINKS
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FORMULA
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MATHEMATICA
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A339891[n_]:=If[n==1, 1, DivisorSum[2n+1, 2^((#-1)/2)&]+DivisorSigma[0, n+1]-2^(n-1)-1]; Array[A339891, 50] (* Paolo Xausa, Dec 04 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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