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Revision History for A054630

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Showing entries 1-10 | older changes

A054630

T(n,k) = Sum_{d|k} phi(d)*n^(k/d)/k, triangle read by rows, T(n,k) for n >= 1 and 1 <= k <= n.
(history; published version)

#65 by Alois P. Heinz at Fri Mar 22 19:07:18 EDT 2024

STATUS

proposed

approved

#64 by Jon E. Schoenfield at Fri Mar 22 19:05:59 EDT 2024

STATUS

editing

proposed

#63 by Jon E. Schoenfield at Fri Mar 22 19:05:49 EDT 2024

	COMMENTS	`T(n, k) areis the number of n-ary necklaces of length k (see Ruskey, Savage and Wang). - Peter Luschny, Aug 12 2012, comment corrected at onthe suggestion of Petros Hadjicostas, Peter Luschny, Sep 10 2018`
	LINKS	`Peter Luschny, <a href="/A054630/a054630.txt">Implementation of the FKM algorithm in SageMath and Julia</a>>.`
	EXAMPLE	`0000,0001,0002,0011,0012,0021,0022,0101,0102,0111,0112,0121,` `0122,0202,0211,0212,0221,0222,1111,1112,1122,1212,1222,2222.` `000,001,002,003,011,012,013,021,022,023,031,032,` `033,111,112,113,122,123,132,133,222,223,233,333.`
	STATUS	`approved` `editing`

#62 by Peter Luschny at Thu Mar 05 10:37:44 EST 2020

STATUS

reviewed

approved

#61 by Michel Marcus at Thu Mar 05 10:16:56 EST 2020

STATUS

proposed

reviewed

#60 by F. Chapoton at Thu Mar 05 09:39:56 EST 2020

STATUS

editing

proposed

#59 by F. Chapoton at Thu Mar 05 09:39:47 EST 2020

PROG

print [([A054630(n, k) for k in (1..n)] # _)]) # _Peter Luschny_, Aug 12 2012

STATUS

approved

editing

Discussion
Thu Mar 05	09:39	F. Chapoton: adapt sage code for py3

#58 by Peter Luschny at Wed Sep 12 16:37:32 EDT 2018

STATUS

proposed

approved

#57 by Petros Hadjicostas at Wed Sep 12 16:15:51 EDT 2018

STATUS

editing

proposed

Discussion
Wed Sep 12	16:37	Peter Luschny: That's fine, thanks!

#56 by Petros Hadjicostas at Wed Sep 12 16:07:07 EDT 2018

	REFERENCES	`H. Fredricksen and I. J. Kessler, An algorithm for generating necklaces of beads in two colors, Discrete Math. 61 (1986), 181-188.`
	LINKS	`D. E. Knuth, Generating All Tuples and Permutations. The Art of Computer Programming, Vol. 4, Fascicle 2, Addison-Wesley, 2005.`

Discussion

Wed Sep 12

16:15

Petros Hadjicostas: Hi Peter, I put a link to the paper by Fredricksen and Kessler. It is weird. It was referenced in 1978 as a paper to appear, but it appeared 6 years later! I also moved the Knuth reference to "REFERENCES" because it has no link. (In the next few days, I will create another sequence based on what you suggested.) - Petros

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Last modified August 27 22:30 EDT 2024. Contains 375471 sequences. (Running on oeis4.)