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Search: id:A129922
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| A129922 |
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Number of 3-Carlitz compositions of n (or, more generally p-Carlitz compositions, p>1) i.e. words b_1^{i_1)b_2^{i_2}...b_k^{i_k} such that b_j's and i_j's are positive integers for which sum(j=1..k i_j*b_j)=n and for all j i_j < p and if b_j=b_{j+1} then i_j+i_{j+1} is not equal to p. The example is for p=3. |
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1
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| 1, 1, 3, 4, 12, 22, 51, 101, 225, 465, 1008, 2111, 4528, 9560, 20402, 43222, 92018, 195256, 415243, 881758, 1874288
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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For p=2 the sequence enumerates Carlitz compositions, A003242
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REFERENCES
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S. Corteel, P. Hitczenko, Generalizations of Carlitz compositions, preprint.
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FORMULA
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for general p the generating function = 1/(1-sum( k>0 z^k/(1-z^k)-p*z^(k*p)/(1-z^(k*p))))
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EXAMPLE
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for p=3 a(3)=4 because we can write: 3^{1},1^{1}2^{1},2^{1}1^{1}, 1^{1}1^{1}1^{1}
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CROSSREFS
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Cf. A003242.
Sequence in context: A101727 A075220 A075221 this_sequence A005221 A000206 A075223
Adjacent sequences: A129919 A129920 A129921 this_sequence A129923 A129924 A129925
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KEYWORD
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nonn
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AUTHOR
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pawel hitczenko (phitczenko(AT)math.drexel.edu), Jun 05 2007
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