

A239132


Pattern of word endings in the lines of a Sestina.


0



1, 2, 3, 4, 5, 6, 6, 1, 5, 2, 4, 3, 3, 6, 4, 1, 2, 5, 5, 3, 2, 6, 1, 4, 4, 5, 1, 3, 6, 2, 2, 4, 6, 5, 3, 1
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OFFSET

1,2


COMMENTS

In a sestina (see the Wikipedia link), which consists of six stanzas of six lines each, the last words in the lines obey the following rule. Denote the six end words of stanza I by 1, 2, 3, 4, 5, 6; then, in stanza II, the six end words are 6, 1, 5, 2, 4, 3; in stanza III, they are 3, 6, 4, 1, 2, 5; in stanza IV: 5, 3, 2, 6, 1, 4; in stanza V: 4, 5, 1, 3, 6, 2; and in stanza VI: 2, 4, 6, 5, 3, 1.
The pattern of a stanza is obtained from the previous stanza by application of the cyclic permutation, which in cycle notation is (1,6,3,5,4,2). (Another way of finding this pattern is called "bottomup pairing", yet another one "backward crossing", see Wikipedia.)
The six stanzas are normally followed by a threeline envoi (or tercet). It would seem logical to apply the cyclic permutation once more, to get the pattern for the two words of the three lines as 1, 2; 3, 4; 5, 6. But in the example of Dante, given in D. Tammet's book, the pattern of the tercet is 2, 1; 4, 6; 5, 3, obtained by applying the permutation (2) (41356) to the pattern of stanza VI.


REFERENCES

Daniel Tammet, Thinking in Numbers. How Maths Illuminates Our Lives, Hodder & Stoughton, London, 2012. German translation: Die Poesie der Primzahlen, Hanser, 2014, Ch. 8, pp. 217228.


LINKS

Table of n, a(n) for n=1..36.
Wikipedia, Sestina.


CROSSREFS

Sequence in context: A228732 A331173 A307089 * A307311 A272081 A317582
Adjacent sequences: A239129 A239130 A239131 * A239133 A239134 A239135


KEYWORD

nonn,full,fini


AUTHOR

Wolfdieter Lang, Apr 05 2014


STATUS

approved



