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Search: id:A032121
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| A032121 |
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Number of reversible strings with n beads of 4 colors. |
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+0
6
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| 4, 10, 40, 136, 544, 2080, 8320, 32896, 131584, 524800, 2099200, 8390656, 33562624, 134225920, 536903680, 2147516416, 8590065664, 34359869440, 137439477760, 549756338176, 2199025352704, 8796095119360
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the number of 4-ary strings of length m = n+1 with number of 1's, 2's and 3's all even. Bijective proof anyone? - Frank Ruskey (fruskey(AT)cs.uvic.ca), Jul 14 2002
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LINKS
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C. G. Bower, Transforms (2)
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FORMULA
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"BIK" (reversible, indistinct, unlabeled) transform of 4, 0, 0, 0...
a(n) = (4^m+3*2^m+(-2)^m)/8, where m = n+1. - Frank Ruskey (fruskey(AT)cs.uvic.ca), Jul 14 2002
G.f.: 2*x*(2-3*x-8*x^2)/((2*x+1)*(2*x-1)*(4*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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EXAMPLE
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a(2) = 10 = |{000, 110,101,011, 220,202,022, 330,303,033}|
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CROSSREFS
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Sequence in context: A149208 A149209 A053792 this_sequence A149210 A149211 A149212
Adjacent sequences: A032118 A032119 A032120 this_sequence A032122 A032123 A032124
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net)
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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