A248604 Numbers a(n) which are the minimum number of moves needed in a variation of the tower of Hanoi with 4 towers and n disks.

1, 3, 5, 9, 13, 21, 37, 69, 133, 261, 517, 1029, 2053, 4101, 8197, 16389, 32773, 65541, 131077, 262149, 524293, 1048581, 2097157, 4194309, 8388613, 16777221, 33554437, 67108869, 134217733, 268435461, 536870917, 1073741829, 2147483653, 4294967301, 8589934597

Offset

1,2

Links

Stefano Spezia, Table of n, a(n) for n = 1..3300

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(1)=1; a(2)=3; a(3)=5; a(n) = 5 + 2^(n-2) for n > 3.

G.f.: x*(1 - 2*x^2 - 4*x^4)/((1 - x)*(1 - 2*x)). - Stefano Spezia, May 15 2023

Mathematica

LinearRecurrence[{3, -2}, {1, 3, 5, 9, 13}, 40] (* Harvey P. Dale, May 10 2019 *)

Crossrefs

Cf. A168614.

Sequence in context: A354788 A187212 A141325 * A146905 A052282 A001993

Adjacent sequences: A248601 A248602 A248603 * A248605 A248606 A248607

Keyword

nonn,easy

Author

Aaron C. Horak, Oct 09 2014

Extensions

More terms from Harvey P. Dale, May 10 2019

Status

approved