

A279685


The maximum number of coins that can be processed in n weighings of an adaptive strategy that all are real (and identical) except for one LHRcoin starting in an unknown state.


5



1, 1, 3, 6, 16, 39, 91, 216, 499, 1144, 2651, 6152, 14227, 32904, 76187, 176376, 408179, 944728, 2186779, 5061544, 11715219, 27116008, 62762971, 145270808, 336242675, 778266424, 1801373403, 4169451080, 9650594451, 22337231432, 51701672731
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OFFSET

0,3


COMMENTS

An LHRcoin is a coin that can change its weight periodically from light to heavy to real to light.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Tanya Khovanova and Konstantin Knop, Coins that Change Their Weights, arXiv:1611.09201 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (3,3,5,4).


FORMULA

a(n) = (A279673(n1) + 1)/2 + A279673(n2), for n > 6.
From Colin Barker, Dec 17 2016: (Start)
a(n) = 3*a(n1)  3*a(n2) + 5*a(n3)  4*a(n4) for n>9.
G.f.: (1  2*x + 3*x^2  5*x^3 + 6*x^4  2*x^5 + 4*x^6 + 4*x^7  7*x^8  4*x^9) / ((1  x)*(1  2*x + x^2  4*x^3)).
(End)


PROG

(PARI) Vec((1  2*x + 3*x^2  5*x^3 + 6*x^4  2*x^5 + 4*x^6 + 4*x^7  7*x^8  4*x^9) / ((1  x)*(1  2*x + x^2  4*x^3)) + O(x^40)) \\ Colin Barker, Dec 17 2016


CROSSREFS

Cf. A279673, A279674, A279682, A279684.
Sequence in context: A275207 A073079 A143560 * A001675 A248091 A168317
Adjacent sequences: A279682 A279683 A279684 * A279686 A279687 A279688


KEYWORD

nonn,easy


AUTHOR

Tanya Khovanova and Konstantin Knop, Dec 16 2016


STATUS

approved



