A334307 Number of graceful labelings for the complete tripartite graph K_1,1,n.

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

Adjacent sequences: A334304 A334305 A334306 * A334308 A334309 A334310

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