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Search: id:A139210
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| A139210 |
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Number of recursively 3-palindromic words of length n over an alphabet of 2 letters. |
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1
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| 2, 2, 4, 4, 8, 4, 8, 8, 16, 16, 32, 16, 32, 16, 64, 32, 64, 16, 32, 32, 64, 64, 128, 64, 128, 128, 256, 256, 512, 256, 512, 256, 1024, 512, 1024, 256, 512, 256, 1024, 512, 2048, 256, 1024, 512, 4096, 2048, 4096, 1024, 2048, 512, 4096, 1024, 2048, 256, 512, 512
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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We define a word of length n to be recursively 3-palindromic if it is empty, or it is a palindrome and its left third and right third of lengths Floor[n/3] and the remaining middle of length n-2Floor[n/3] are all recursively 3-palindromic.
See the Ji/Wilf reference for the definition of a recursively palindromic sequence. The number of recursively palindromic words of length n over an alphabet of 2 letters is given in A001316.
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REFERENCES
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Kathy Q. Ji and Herbert S. Wilf, Extreme Palindromes, Am. Math. Monthly 115 (2008) 447-451.
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FORMULA
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a(1)=2, a(2)=2 and, for n>2, a(n)=a([n/3])*a(n-2[n/3])., where [...] denotes the floor or greatest integer function.
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EXAMPLE
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{0,0,0,0,0,0,0}, {0,0,0,1,0,0,0}, {0,0,1,0,1,0,0}, {0,0,1,1,1,0,0}, {1,1,0,0,0,1,1}, {1,1,0,1,0,1,1}, {1,1,1,0,1,1,1}, {1,1,1,1,1,1,1} are the eight recursively 3-palindromic words of length seven over an alphabet of two letters, so a(7)=8.
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CROSSREFS
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Cf. A001316.
Adjacent sequences: A139207 A139208 A139209 this_sequence A139211 A139212 A139213
Sequence in context: A032190 A005852 A115209 this_sequence A008330 A138219 A100835
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jun 06 2008
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