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A334307
Number of graceful labelings for the complete tripartite graph K_{1,1,n}.
3
12, 32, 168, 1152, 9600, 97920, 1491840, 21127680, 377395200, 7605964800, 164457216000, 3935477145600, 102571486617600, 2858053098700800, 85725900868608000, 2745404797943808000, 93266934645620736000, 3356738924418367488000, 127589166595209166848000
OFFSET
1,1
COMMENTS
Except for n = 2, a(n) = A333728(n+2) up to at least n = 6.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..400 (terms 1..48 from Don Knuth)
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Graceful Labeling
FORMULA
If n>1, a(n) = 4*A339891(n)*n!. - Don Knuth, Dec 21 2020.
MATHEMATICA
A334307[n_]:=If[n==1, 12, 4n!(DivisorSum[2n+1, 2^((#-1)/2)&]+DivisorSigma[0, n+1]-2^(n-1)-1)]; Array[A334307, 25] (* Paolo Xausa, Dec 04 2023 *)
CROSSREFS
Cf. A333728 (maximum number of graceful labelings for an n-node simple graph), A339891.
Sequence in context: A268769 A045669 A045660 * A192213 A050690 A079561
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 24 2020
EXTENSIONS
a(8) and a(9) from Pontus von Brömssen, Jul 25 2020
Terms a(10) and beyond from Don Knuth, Dec 21 2020
STATUS
approved