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%I #14 Jan 24 2024 10:56:55
%S 0,1,1,16,32,729,2187,65536,262144,9765625,48828125,2176782336,
%T 13060694016,678223072849,4747561509943,281474976710656,
%U 2251799813685248,150094635296999121,1350851717672992089,100000000000000000000,1000000000000000000000,81402749386839761113321
%N a(n) = floor(n/2)^n.
%C The sequence gives the number of (potentially unsolvable) "clock puzzles" with n positions in the video game Final Fantasy XIII-2.
%C Functions from [n] to [n] with f(i) even or f(i) = 1 for all i. - _Olivier Gérard_, Sep 23 2016
%C AGM transform of A059841. See A368366 for the definition of the AGM transform. - _Alois P. Heinz_, Jan 24 2024
%H G. C. Greubel, <a href="/A206344/b206344.txt">Table of n, a(n) for n = 1..425</a>
%H N. Johnston, <a href="http://www.njohnston.ca/2012/02/counting-and-solving-final-fantasy-xiii-2s-clock-puzzles/">Counting and Solving Final Fantasy XIII-2's Clock Puzzles</a>
%p seq(floor(n/2)^n, n=1..50);
%t Table[Floor[n/2]^n, {n,30}]
%o (Magma) [Floor(n/2)^n: n in [1..30]]; // _G. C. Greubel_, Mar 31 2023
%o (SageMath) [(n//2)^n for n in range(1,31)] # _G. C. Greubel_, Mar 31 2023
%Y Cf. A206345, A206346, A276978, A276979 (other classes of endofunctions defined by image parity).
%Y Cf. A059841, A368366.
%K nonn,easy
%O 1,4
%A _Nathaniel Johnston_, Feb 06 2012
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