A078707 Number of vectors of length n that are symmetric about the middle, where each element is drawn from a set of n distinct elements.

1, 1, 2, 9, 16, 125, 216, 2401, 4096, 59049, 100000, 1771561, 2985984, 62748517, 105413504, 2562890625, 4294967296, 118587876497, 198359290368, 6131066257801, 10240000000000, 350277500542221, 584318301411328, 21914624432020321, 36520347436056576

Offset: 0

Author

Mark Sterling, Dec 18 2002

Keywords

• nonn
• easy

Examples

			Examples added by _N. J. A. Sloane_, Jun 17 2014:
n=1: 1 (1).
n=2: 11, 22 (2).
n=3: 111X3, 121X6 (9).
n=4: 1111X4, 1221X12 (16).
n=5: 11111X5, 11211X20, 12221X20, 12121X20, 12321X60 (125).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A004526, A243520.

Cf. A168658, A275549.

This is for Coxeter type B what A152291 is for Coxeter type A.

Programs

Maple

a:= n-> n^ceil(n/2): seq(a(n), n=0..30);  # Alois P. Heinz, Jul 23 2014

Mathematica

Join[{1}, Table[n^Ceiling[n/2], {n, 30}]] (* Wesley Ivan Hurt, Jan 15 2017 *)

PARI

for(n=1,22,print1(n^((n+n%2)/2),","))

Formula

a(n) = n^(floor((n+1)/2)) = n^ceiling(n/2).

Extensions

Extended by Klaus Brockhaus, Dec 19 2002

a(0)=1 inserted by Alois P. Heinz, Jul 23 2014