A206344 a(n) = floor(n/2)^n.

0, 1, 1, 16, 32, 729, 2187, 65536, 262144, 9765625, 48828125, 2176782336, 13060694016, 678223072849, 4747561509943, 281474976710656, 2251799813685248, 150094635296999121, 1350851717672992089, 100000000000000000000, 1000000000000000000000, 81402749386839761113321

Offset

1,4

Comments

The sequence gives the number of (potentially unsolvable) "clock puzzles" with n positions in the video game Final Fantasy XIII-2.

Functions from [n] to [n] with f(i) even or f(i) = 1 for all i. - Olivier Gérard, Sep 23 2016

AGM transform of A059841. See A368366 for the definition of the AGM transform. - Alois P. Heinz, Jan 24 2024

Links

G. C. Greubel, Table of n, a(n) for n = 1..425

N. Johnston, Counting and Solving Final Fantasy XIII-2's Clock Puzzles

Maple

seq(floor(n/2)^n, n=1..50);

Mathematica

Table[Floor[n/2]^n, {n, 30}]

Prog

(Magma) [Floor(n/2)^n: n in [1..30]]; // G. C. Greubel, Mar 31 2023
(SageMath) [(n//2)^n for n in range(1, 31)] # G. C. Greubel, Mar 31 2023

Crossrefs

Cf. A206345, A206346, A276978, A276979 (other classes of endofunctions defined by image parity).

Cf. A059841, A368366.

Sequence in context: A339356 A282832 A331420 * A119349 A070591 A181452

Adjacent sequences: A206341 A206342 A206343 * A206345 A206346 A206347

Keyword

nonn,easy

Author

Nathaniel Johnston, Feb 06 2012

Status

approved