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A079861
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a(i)=the number of occurrences of 7s in the palindromic compositions of n=2*i-1 = the number of occurrences of 8s in the palindromic compositions of n=2*i.
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6
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10, 22, 48, 104, 224, 480, 1024, 2176, 4608, 9728, 20480, 43008, 90112, 188416, 393216, 819200, 1703936, 3538944, 7340032, 15204352, 31457280, 65011712, 134217728, 276824064, 570425344, 1174405120, 2415919104, 4966055936
(list; graph; refs; listen; history; internal format)
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OFFSET
| 8,1
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COMMENTS
| 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
| Vincenzo Librandi, Table of n, a(n) for n = 8..1000
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
| a(i) = (2+i)*2^(i-8)
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EXAMPLE
| a(8)=10 since the palindromic compositions of 15 that contain a 7 are 7+1+7, 4+7+4, 1+3+7+3+1, 3+1+7+1+3, 2+2+7+2+2, 1+1+1+1+7+1+1+1+1, 1+1+2+7+2+1+1, 1+2+1+7+1+2+1 and 2+1+1+7+1+1+2, for a total of 10 7s.
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MATHEMATICA
| Table[(2 + i)*2^(i - 8), {i, 8, 50}]
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PROG
| (MAGMA) [(2+n)*2^(n-8) : n in [8..40]]; // Vincenzo Librandi, Sep 22 2011
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CROSSREFS
| Cf. A057711, A001792, A079859, A079860, A079862, A079863.
Sequence in context: A157917 A104867 A179877 * A014008 A039315 A088871
Adjacent sequences: A079858 A079859 A079860 * A079862 A079863 A079864
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KEYWORD
| easy,nonn
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AUTHOR
| Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003
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