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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 LHR-coin 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An LHR-coin 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(n-1) + 1)/2 + A279673(n-2), for n > 6.

From Colin Barker, Dec 17 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + 5*a(n-3) - 4*a(n-4) 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

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)