

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
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OFFSET

0,2


COMMENTS

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 kth disk solving (nonoptimally) the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] precolored Magnetic Tower of Hanoi puzzle (see the "CROSSREFS" in A183120). For other Magnetic Tower of Hanoi related sequences Cf. A183111A183125.
Same as A052919 except first term is 1, not 2.  Omar E. Pol, Feb 20 2011


REFERENCES

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


LINKS

Table of n, a(n) for n=0..25.
Uri Levy, The Magnetic Tower of Hanoi, arXiv:1003.0225 [math.CO], 2010.
Index entries for linear recurrences with constant coefficients, signature (4, 3).


FORMULA

For n>1, a(n) = 3*a(n1)2.
a(n)=1+2*3^(n1), n>0. a(n)=4*a(n1)3*a(n2), n>2. G.f.: (1+x)*(2*x1)/((3*x1)*(x1)).  R. J. Mathar, Jun 30 2009


MATHEMATICA

Join[{1}, LinearRecurrence[{4, 3}, {3, 7}, 25]] (* JeanFrançois Alcover, Jul 28 2018 *)


PROG

(PARI) a(n)=([0, 1; 3, 4]^n*[1; 3])[1, 1] \\ Charles R Greathouse IV, Jan 28 2018


CROSSREFS

Cf. A052919.
Sequence in context: A115760 A183115 A183120 * A224031 A147586 A305197
Adjacent sequences: A100699 A100700 A100701 * A100703 A100704 A100705


KEYWORD

easy,nonn


AUTHOR

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


STATUS

approved



