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A056450
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Number of palindromes of length n using a maximum of four different symbols.
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14
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4, 4, 16, 16, 64, 64, 256, 256, 1024, 1024, 4096, 4096, 16384, 16384, 65536, 65536, 262144, 262144, 1048576, 1048576, 4194304, 4194304, 16777216, 16777216, 67108864, 67108864, 268435456, 268435456
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OFFSET
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1,1
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index to divisibility sequences
Index to sequences with linear recurrences with constant coefficients, signature (0,4)
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FORMULA
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a(n) = 4^floor((n+1)/2).
G.f.: -4*x*(1+x) / ( (2*x-1)*(2*x+1) ). - R. J. Mathar, Jan 19 2011
a(n) = 4*abs(A164111(n-1)). - R. J. Mathar, Jan 19 2011
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EXAMPLE
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At length n=1 there are a(1)=4 palindromes, A, B, C, D. At length n=2, there are a(2)=4 palindromes, AA, BB, CC, DD. At length n=3, there are a(3)=16 palindromes, AAA, BBB, CCC, DDD, ABA, BAB, ... , CDC, DCD.
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PROG
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(MAGMA) [4^Floor((n+1)/2): n in [1..40]]; // Vincenzo Librandi, Aug 16 2011
(PARI) a(n)=4^((n+1)\2) \\ Charles R Greathouse IV, Apr 08 2012
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CROSSREFS
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Cf. A016116.
Sequence in context: A220761 A218522 * A141125 A164111 A164906 A213173
Adjacent sequences: A056447 A056448 A056449 * A056451 A056452 A056453
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KEYWORD
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nonn,easy
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AUTHOR
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Marks R. Nester (nesterm(AT)dpi.qld.gov.au)
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STATUS
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approved
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