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A006967 Number of graceful permutations of length n.
(Formerly M3229)
8
1, 2, 4, 4, 8, 24, 32, 40, 120, 296, 648, 1328, 3200, 9912, 25592, 55920, 143192, 510696, 1451296, 3497344, 10451824, 38570704, 118914992, 315235872, 1014824752, 3963684496, 13166130152, 37846301904, 130507967088, 533318630936, 1884550215976, 5800121391936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. S. Wilf and N. Yoshimura, Ranking rooted trees and a graceful application, in Discrete Algorithms and Complexity (Proceedings of the Japan-US joint seminar, 1986, Kyoto, Japan), edited by D. Johnson, T. Nishizeki, A. Nozaki and H. S. Wilf, Academic Press, NY, 1987, pp. 341-350.

LINKS

Michal Adamaszek (aszek(AT)mimuw.edu.pl), Aug 22 2006, Table of n, a(n) for n = 1..40

M. Adamaszek, Efficient enumeration of graceful permutations, arXiv:math/0608513 [math.CO], 2006.

Gheorghe Coserea, Solutions for n=5.

Gheorghe Coserea, Solutions for n=6.

Gheorghe Coserea, MiniZinc model for generating solutions.

Md Masbaul Alam Polash, M. A. Hakim Newton, Abdul Sattar, Constraint-directed search for all-interval series, Constraints, July 2017, Volume 22, Issue 3, pp 403-431. See page 426.

Eric Weisstein's World of Mathematics, Graceful Permutation

J. Wodlinger, Costas arrays, Golomb rulers and wavelength isolation sequence pairs, M.S. Dissertation, Math. Dept., Simon Fraser University, Spring 2012; - From N. J. A. Sloane, Oct 15 2012

FORMULA

a(n) = n! - A084894(n). - Jon Perry, Jun 10 2003

CROSSREFS

Cf. A084894.

Sequence in context: A080007 A239649 A264190 * A296229 A298117 A122033

Adjacent sequences:  A006964 A006965 A006966 * A006968 A006969 A006970

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane

EXTENSIONS

n=2 term corrected June 1996

a(11)-a(20) from Robert Aldred and Brendan McKay

More terms from Michal Adamaszek (aszek(AT)mimuw.edu.pl), Aug 22 2006

STATUS

approved

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Last modified November 17 04:27 EST 2018. Contains 317275 sequences. (Running on oeis4.)