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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

Index to divisibility sequences

Index to sequences with linear recurrences with constant coefficients, signature (0,4)

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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Last modified May 18 19:33 EDT 2013. Contains 225426 sequences.