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A100702
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Number of layers of dough separated by butter in successive foldings of croissant dough.
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7
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1, 3, 7, 19, 55, 163, 487, 1459, 4375, 13123, 39367, 118099, 354295, 1062883, 3188647, 9565939, 28697815, 86093443, 258280327, 774840979, 2324522935, 6973568803, 20920706407, 62762119219, 188286357655, 564859072963
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OFFSET
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0,2
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COMMENTS
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At each trebling of layers following the first, two sets of layers, not separated from their neighbors by butter, are combined. Traditional patisserie stops at 55 layers, but forgetful chefs have been know to make additional folds to 163 layers.
This sequence also describes the number of moves of the k-th disk solving (non-optimally) the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored Magnetic Tower of Hanoi puzzle (see the "CROSSREFS" in A183120). For other Magnetic Tower of Hanoi related sequences Cf. A183111 - A183125.
Same as A052919 except first term is 1, not 2. - Omar E. Pol, Feb 20 2011.
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REFERENCES
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J. Child and M. Beck, Mastering the Art of French Cooking, Vol. 2
Uri Levy, The Magnetic Tower of Hanoi, arXiv:1003.0225.
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LINKS
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Table of n, a(n) for n=0..25.
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FORMULA
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For n>1, a(n) = 3*a(n-1)-2.
a(n)=1+2*3^(n-1), n>0. a(n)=4*a(n-1)-3*a(n-2), n>2. G.f.: -(1+x)*(2*x-1)/((3*x-1)*(x-1)). [From R. J. Mathar, Jun 30 2009]
a(n) = A052919(n) - A000007(n). - Omar E. Pol, Feb 20 2011.
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CROSSREFS
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Cf. A052919. - Omar E. Pol, Feb 20 2011.
Sequence in context: A115760 A183115 A183120 * A224031 A147586 A071716
Adjacent sequences: A100699 A100700 A100701 * A100703 A100704 A100705
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KEYWORD
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easy,nonn
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AUTHOR
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Daniel Wolf (djwolf1(AT)axelero.hu), Dec 09 2004
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EXTENSIONS
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More terms from R. J. Mathar, Jun 30 2009
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STATUS
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approved
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