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

0,3

Links

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

Formula

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

Example

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).

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 *)

Prog

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

Crossrefs

Cf. A004526, A243520.

Cf. A168658, A275549.

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

Sequence in context: A032040 A045661 A369647 * A085332 A204424 A062981

Adjacent sequences: A078704 A078705 A078706 * A078708 A078709 A078710

Keyword

nonn,easy

Author

Mark Sterling, Dec 18 2002

Extensions

Extended by Klaus Brockhaus, Dec 19 2002

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

Status

approved