A260217 Number of base-3 n-digit pandigital numbers.

0, 0, 4, 24, 100, 360, 1204, 3864, 12100, 37320, 114004, 346104, 1046500, 3155880, 9500404, 28566744, 85831300, 257756040, 773792404, 2322425784, 6969374500, 20912317800, 62745342004, 188252803224, 564791964100, 1694443001160, 5083463221204, 15250658099064

Offset

1,3

Comments

From Manfred Boergens, Aug 02 2023: (Start)

a(n+1) is the number of pairs (A,B) where A and B are nonempty subsets of {1,2,...,n} and one of these subsets is a proper subset of the other.

If "proper" is omitted, see A091344.

If empty subsets are included, see A027649 (all subsets) and A056182 (proper subsets). (End)

Links

Table of n, a(n) for n=1..28.

Svenja Huntemann, Values, Temperatures, and Enumeration of Placement Games, Slides, Alberta-Montana Combinatorics and Algorithms Day, Banff, Canada, 23-25 June 2023. See p. 105/109.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = 2*A028243(n) = 2*3^(n-1) - 2^(n+1) + 2.

a(n) = 4*A000392(n).

G.f.: 4*x^3/((1-x)*(1-2*x)*(1-3*x)).

E.g.f.: 2/3*((exp(x)-1)^3).

Example

a(3)=4 because, in base 3, there are four 3-digit pandigital numbers (11=102_3, 15=120_3, 19=201_3, and 21=210_3).
a(4)=24 because, in base 3, there are 24 4-digit pandigital numbers (1002_3, 1012_3, 1020_3, 1021_3, 1022_3, 1102_3, 1120_3, 1200_3, 1201_3, 1202_3, 1210_3, 1220_3, 2001_3, 2010_3, 2011_3, 2012_3, 2021_3, 2100_3, 2101_3, 2102_3, 2110_3, 2120_3, 2201_3, and 2210_3).

Mathematica

Table[2 3^(n - 1) - 2^(n + 1) + 2, {n, 30}] (* Vincenzo Librandi, Jul 20 2015 *)

Prog

(Magma) [2*3^(n-1) - 2^(n+1) + 2: n in [1..30]]; // Vincenzo Librandi, Jul 20 2015

Crossrefs

Cf. A000392, A027649, A028243, A056182, A091344, A171102.

Sequence in context: A139238 A139231 A052462 * A048806 A043009 A355798

Adjacent sequences: A260214 A260215 A260216 * A260218 A260219 A260220

Keyword

nonn,base

Author

Jon E. Schoenfield, Jul 19 2015

Status

approved