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Search: id:A141783
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| A141783 |
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Number of bracelets with n beads: one blue, g green, and r = n-(g+1) red, for g = 12. |
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+0
1
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| 1, 7, 49, 231, 924, 3108, 9324, 25236, 63090, 147070, 323554, 676270, 1352540, 2600612, 4829708, 8692788, 15212379, 25949469, 43249115, 70562765, 112900424, 177412664, 274183208, 417232088, 625848132, 926250780, 1353751140
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OFFSET
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13,2
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COMMENT
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With offset g+1, the sequence a(n) of the numbers of bracelets with g green, and r = n-g-1 red beads is given by the formula of the paraffin numbers l(c,r) replacing c by g+3.
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LINKS
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Harold S. Grant, On a Formula for Circular Permutations.
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FORMULA
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a(n) = 1/2*(C(n-1,12) + C((n-2+n mod 2)/2, 6)).
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EXAMPLE
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The seven bracelets with 14 beads - 1 blue(B), 12 green(G), and 1 red(R) can be represented by the strings BGGGGGGGGGGGGR, BGGGGGGGGGGGRG, BGGGGGGGGGGRGG, BGGGGGGGGGRGGG, BGGGGGGGGRGGGG, BGGGGGGGRGGGGG, and BGGGGGGRGGGGGG.
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PROGRAM
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(PARI) g = 12 K = binomial(n-1, g)/2 a(n)= if(n%2*(g%2)==1, K, K+binomial((n-2+n%2)/2, (g-g%2)/2)/2)
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CROSSREFS
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Cf. A005993, A005994, A005995, A018210, A018211, A018212, A018213, A018214, A002620, A062136.
Sequence in context: A003530 A015953 A133047 this_sequence A094430 A146884 A113235
Adjacent sequences: A141780 A141781 A141782 this_sequence A141784 A141785 A141786
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KEYWORD
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easy,nonn
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AUTHOR
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Washington Bomfim (webonfim(AT)bol.com.br), Aug 17 2008
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