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A100702 Number of layers of dough separated by butter in successive foldings of croissant dough. 7
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 (list; graph; refs; listen; history; text; internal format)



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.


J. Child and M. Beck, Mastering the Art of French Cooking, Vol. 2


Table of n, a(n) for n=0..25.

Uri Levy, The Magnetic Tower of Hanoi, arXiv:1003.0225.

Index entries for linear recurrences with constant coefficients, signature (4, -3).


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]


Cf. A052919.

Sequence in context: A115760 A183115 A183120 * A224031 A147586 A071716

Adjacent sequences:  A100699 A100700 A100701 * A100703 A100704 A100705




Daniel Wolf (djwolf1(AT)axelero.hu), Dec 09 2004



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Last modified November 28 09:50 EST 2015. Contains 264557 sequences.