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 A056450 Number of palindromes of length n using a maximum of four different symbols. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 FORMULA 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 EXAMPLE 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. PROG (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 CROSSREFS Cf. A016116. Sequence in context: A220761 A218522 * A141125 A164111 A164906 A213173 Adjacent sequences:  A056447 A056448 A056449 * A056451 A056452 A056453 KEYWORD nonn,easy AUTHOR Marks R. Nester (nesterm(AT)dpi.qld.gov.au) STATUS approved

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