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Search: id:A003242
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| A003242 |
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Number of compositions of n such that no two adjacent parts are equal. |
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+0
29
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| 1, 1, 1, 3, 4, 7, 14, 23, 39, 71, 124, 214, 378, 661, 1152, 2024, 3542, 6189, 10843, 18978, 33202, 58130, 101742, 178045, 311648, 545470, 954658, 1670919, 2924536, 5118559, 8958772, 15680073, 27443763, 48033284, 84069952, 147142465, 257534928, 450748483, 788918212
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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L. Carlitz, Restricted Compositions, Fibonacci Quarterly, 14 (1976) 254-264.
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LINKS
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Christian G. Bower, Table of n, a(n) for n = 0..500
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 201
A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
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FORMULA
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a(n)=Sum_{k=1..n} A048272(k)*a(n-k), n>1, a(0)=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2002
G.f. 1/(1 - sum(k>0, x^k/(1+x^k))).
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CROSSREFS
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Cf. A106351, A114900, A114902.
Sequence in context: A041002 A062203 A095063 this_sequence A073728 A132407 A070035
Adjacent sequences: A003239 A003240 A003241 this_sequence A003243 A003244 A003245
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KEYWORD
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nonn,nice
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AUTHOR
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erc(AT)pollux.cs.uga.edu (E Rodney Canfield)
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net).
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