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A056487
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a(n)=5^(n/2) for n even, a(n)=3*5^((n-1)/2) for n odd.
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5
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1, 3, 5, 15, 25, 75, 125, 375, 625, 1875, 3125, 9375, 15625, 46875, 78125, 234375, 390625, 1171875, 1953125, 5859375, 9765625, 29296875, 48828125, 146484375, 244140625, 732421875, 1220703125, 3662109375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of periodic palindromes using a maximum of five different symbols. For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.
Apparently identical to A111386! Is this a theorem? - Klaus Brockhaus, (klaus-brockhaus(AT)t-online.de), Jul 21 2009
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REFERENCES
| M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,5).
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FORMULA
| a(n+2)=5a(n), a(0)=1, a(2)=3.
Binomial transform of A087205. Binomial transform is A087206. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003
G.f.: (1+3x)/(1-5x^2); a(n)=5^(n/2)(1/2+3sqrt(5)/10+(1/2-3sqrt(5)/10)(-1)^n). - Paul Barry (pbarry(AT)wit.ie), Mar 19 2004
2nd inverse binomial transform of Fib(3n+2). - Paul Barry (pbarry(AT)wit.ie), Apr 16 2004
a(n+3) = a(n+2)*a(n+1)/a(n). [Reinhard Zumkeller, Mar 04 2011]
a(n) = 3^((1-(-1)^n)/2) * 5^((2*n+(-1)^n-1)/4) - Bruno Berselli, Mar 24 2011
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PROG
| (MAGMA) [n le 2 select 2*n-1 else 5*Self(n-2): n in [1..28]]; // Bruno Berselli, Mar 24 2011
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CROSSREFS
| Cf. A029744, A038754, A056451.
Sequence in context: A108814 A018272 A018421 * A163114 A111386 A146582
Adjacent sequences: A056484 A056485 A056486 * A056488 A056489 A056490
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KEYWORD
| nonn
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AUTHOR
| Marks R. Nester (nesterm(AT)dpi.qld.gov.au)
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EXTENSIONS
| Changed one 'even' to 'odd' in the definition - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 06 2010
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