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A089746
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Period 12: repeat (4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3). (Number of syllables in English name of the months.)
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4
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4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3
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OFFSET
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1,1
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COMMENTS
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Original definition: Number of syllables in English name of n-th month, with comment: Period 12.
The original definition corresponds to the finite subsequence a(1)..a(12). There is no 13th month of the year. If "of the year" is omitted on purpose, there's no reason that the 1st month be January: the first day of the currently used Gregorian calendar was October 15, 1582, so the 1st month should be October. Originally the first month was March (whence the names September, ..., December for the 7th, ..., 10th month) and January was the 11th month. - M. F. Hasler, Feb 25 2018
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REFERENCES
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Marilyn vos Savant (marilyn(AT)parade.com), column in Parade magazine, 2003.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).
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FORMULA
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G.f.: x*(-3*x^11 - 3*x^10 - 3*x^9 - 3*x^8 - 2*x^7 - 2*x^6 - x^5 - x^4 - 2*x^3 - x^2 - 4*x - 4)/(x^12 - 1). - Chai Wah Wu, Feb 16 2021
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EXAMPLE
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For example, January is pronounced with four syllables: Jan-u-ar-y.
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PROG
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(PARI) a(n)=digits(344121122333)[n%12+1] \\ M. F. Hasler, Feb 25 2018
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CROSSREFS
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KEYWORD
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nonn,word
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AUTHOR
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Drexel Hallaway (drexel(AT)cs.columbia.edu), Jan 08 2004
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EXTENSIONS
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Thanks to Ray Chandler for supplying the explanation for this sequence.
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STATUS
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approved
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