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Revision History for A003242 (Underlined text is an addition; strikethrough text is a deletion.)

Showing entries 1-10 | older changes
A003242 Number of compositions of n such that no two adjacent parts are equal (these are sometimes called Carlitz compositions).
(history; published version)
#122 by N. J. A. Sloane at Fri Aug 16 20:51:37 EDT 2024
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editing

approved

#121 by N. J. A. Sloane at Fri Aug 16 20:51:35 EDT 2024
NAME

Number of compositions of n such that no two adjacent parts are equal (these are sometimes called Carlitz compositions).

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approved

editing

#120 by Alois P. Heinz at Fri Oct 27 18:27:45 EDT 2023
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editing

approved

#119 by Alois P. Heinz at Fri Oct 27 18:27:41 EDT 2023
LINKS

Christian G. Bower and Alois P. Heinz, <a href="/A003242/b003242.txt">Table of n, a(n) for n = 0..4100</a> (first 501 terms from Christian G. Bower)

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approved

editing

#118 by Michael De Vlieger at Wed Aug 23 08:34:57 EDT 2023
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proposed

approved

#117 by Michel Marcus at Wed Aug 23 05:42:30 EDT 2023
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editing

proposed

#116 by Michel Marcus at Wed Aug 23 05:42:26 EDT 2023
LINKS

Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022, p. 42 and 117.

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approved

editing

#115 by Joerg Arndt at Tue May 24 10:08:42 EDT 2022
COMMENTS

For N=2n+k, with k even and k>n, a(n) is the number of Carlitz palindromic compositions having k as a central summand. For N=2n+1+k, with k odd and k>n, a(n) is the number of palindromic compositions having k as a central summand. - Gregory L. Simay, May 15 2022

EXAMPLE

Enumerate the Carlitz palindrome compositions of 13 for which the central summand is the greatest part: 13; 1,11,1; 2,9,2; 3,7,3 & 2,1,7,1,2 & 1,2,7,2,1; and 4,5,4 & 3,1,5,1,3 & 1,3,5,3,1 & 1,2,1,5,1,2,1. Note that in these instances, the number of Carlitz palindromes so enumerated is 1+1+1+3+4 = a(0) + a(1) + a(2) + a(3) + a(4). - Gregory L. Simay, May 15 2022

CROSSREFS

Cf. A239327, Carlitz palindromic compositions. -Gregory L. Simay, May 07 2022

KEYWORD

nonn,nice,changed

STATUS

editing

approved

#114 by Joerg Arndt at Wed May 18 08:01:55 EDT 2022
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proposed

editing

Discussion
Tue May 24 10:08
Joerg Arndt: grrrr...  reverting now.
#113 by Michel Marcus at Wed May 18 00:45:01 EDT 2022
STATUS

editing

proposed

Discussion
Wed May 18 08:01
Joerg Arndt: So you comment does not belong here but to the sequence of partial sums?

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Last modified August 29 06:09 EDT 2024. Contains 375510 sequences. (Running on oeis4.)