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Search: id:A079863
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| A079863 |
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a(i)=the number of occurrences of 11s in the palindromic compositions of n=2*i-1 = the number of occurrences of 12s in the palindromic compositions of n=2*i. |
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5
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| 34, 70, 144, 296, 608, 1248, 2560, 5248, 10752, 22016, 45056, 92160, 188416, 385024, 786432, 1605632, 3276800, 6684672, 13631488, 27787264, 56623104, 115343360, 234881024, 478150656, 973078528, 1979711488, 4026531840
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OFFSET
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12,1
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COMMENT
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This sequence is part of a family of sequences, namely R(n,k), the number of ks in palindromic compositions of n. See also A057711, A001792, A078836, A079861, A079862. General formula: R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k) if n and k have different parity and R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k + 2^(floor((k+1)/2 - 1)) otherwise, for n >= 2k.
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LINKS
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P. Chinn, R. Grimaldi and S. Heubach, The frequency of summands of a particular size ..., Ars Combin. 69 (2003), 65-78.
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FORMULA
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a(i) = (i+22)*2^(i-12)
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EXAMPLE
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a(12)=34 since the palindromic compositions of 23 that contain a 11 are 11+1+11 and the 32 compositions of the form c+11+(reverse of c), where c represents a composition of 6.
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MATHEMATICA
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Table[(22 + i)*2^(i - 12), {i, 12, 50}]
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CROSSREFS
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Cf. A057711, A001792, A079859 - A079862.
Sequence in context: A044136 A044517 A063333 this_sequence A154095 A063533 A118619
Adjacent sequences: A079860 A079861 A079862 this_sequence A079864 A079865 A079866
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KEYWORD
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easy,nonn
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AUTHOR
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Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003
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