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

Author

Jon E. Schoenfield, Jul 19 2015

Keywords

• nonn
• base

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)

Examples

			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).
		

Links

• 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).

Crossrefs

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

Programs

Magma

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

Mathematica

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

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).