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6, 14, 32, 72, 160, 352, 768, 1664, 3584, 7680, 16384, 34816, 73728, 155648, 327680, 688128, 1441792, 3014656, 6291456, 13107200, 27262976, 56623104, 117440512, 243269632, 503316480, 1040187392, 2147483648, 4429185024, 9126805504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,1
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COMMENTS
| a(n) = the number of occurrences of 5s in the palindromic compositions of 2n-1 = the number of occurrences of 6s in the palindromic compositions of 2n.
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, A079859, A079861 - A079863. 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 = 0..3000
P. Chinn, R. Grimaldi and S. Heubach, The frequency of summands of a particular size ..., Ars Combin. 69 (2003), 65-78.
Index to sequences with linear recurrences with constant coefficients, signature (4,-4).
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EXAMPLE
| a(6)=6 since the palindromic compositions of 11 that contain a 5 are 3+5+3, 1+2+5+2+1, 2+1+5+1+2, 1+1+1+5+1+1+1 and 5+1+5, for a total of 6 5s. The palindromic compositions of 12 that contain a 6 are 3+6+3, 1+2+6+2+1, 2+1+6+1+2, 1+1+1+6+1+1+1 and 6+6.
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MATHEMATICA
| Table[i*2^(i-6), {i, 6, 50}]
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PROG
| (PARI) a(n)=n<<(n-6) \\ Charles R Greathouse IV, Oct 03 2011
(MAGMA) [n*2^(n-6): n in [6..40]]; // Vincenzo Librandi, Oct 04 2011
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CROSSREFS
| Cf. A057711, A001792, A079859, A079861-A079863.
Sequence in context: A134067 A024932 A199705 * A142875 A074981 A066510
Adjacent sequences: A078833 A078834 A078835 * A078837 A078838 A078839
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KEYWORD
| easy,nonn
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AUTHOR
| Silvia Heubach (sheubac(AT)calstatela.edu), Jan 17 2003
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