

A339891


Number of fundamentally different graceful labelings of the complete tripartite graph K_1,1,n.


2



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

1,2


COMMENTS

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.


REFERENCES

D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation.


LINKS



FORMULA



MATHEMATICA

A339891[n_]:=If[n==1, 1, DivisorSum[2n+1, 2^((#1)/2)&]+DivisorSigma[0, n+1]2^(n1)1]; Array[A339891, 50] (* Paolo Xausa, Dec 04 2023 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



