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.

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

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