A293948 Arises in a coin-weighing problem.

1, 1, 3, 5, 11, 20, 41, 82, 163, 334, 659, 1350, 2667, 5430, 10763, 21782, 43307, 87254, 173867, 349270, 697003, 1397590, 2791595, 5591382, 11174571, 22367574, 44716715, 89474390, 178907819, 357905750, 715721387, 1431639382, 2863082155, 5726590294, 11452754603, 22906426710, 45811935915, 91625837910

Offset

0,3

Comments

Number of coins that can be processed using n weighings with a "Light-Real" coin with the starting state unknown. - Robert Price, Nov 29 2017

Links

Robert Price, Table of n, a(n) for n = 0..201

Tanya Khovanova and Konstantin Knop, Coins that Change Their Weights, arXiv:1611.09201 [math.CO], 2016. See Section 4.

Formula

From Robert Israel, Nov 29 2017: (Start)

a(n) = (2^(n+1)+1)/3 + (1/2-n/8)*2^(n/2) if n>2 is even.

a(n) = (2^(n+1)+2)/3 - 2^((n+1)/2)/4 if n>1 is odd.

G.f.: (1-x-4*x^2+4*x^3+4*x^4-5*x^5+6*x^7-2*x^8-4*x^9)/((1-x^2)*(1-2*x)*(1-2*x^2)^2). (End)

Maple

f:= proc(n) if n::even then (2^(n+1)+1)/3 + (1/2-n/8)*2^(n/2)
else (2^(n+1)+2)/3 - 2^((n+1)/2)/4 fi end proc:
1, 1, 3, seq(f(i), i=3..100); # Robert Israel, Nov 29 2017

Mathematica

Jacobsthal[n_] := (2^n - (-1)^n)/3;
lst = {1, 1, 3, 5};
For[k = 2, k <= 100, k++,
    AppendTo[lst, (Jacobsthal[2*k + 2] - (k - 2)*2^(k - 1) + 1)/2];
    AppendTo[lst, (Jacobsthal[2*k + 3] - 2^k + 1)/2]];
lst

Crossrefs

Sequence in context: A299027 A339006 A247353 * A281318 A082713 A074710

Adjacent sequences: A293945 A293946 A293947 * A293949 A293950 A293951

Keyword

nonn

Author

N. J. A. Sloane, Oct 28 2017

Extensions

Terms a(9) and beyond from Robert Price, Nov 29 2017

Status

approved