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Number of n-digit cycles of length 5 under the Kaprekar map A151949
6

%I #7 Apr 13 2024 22:53:23

%S 0,0,0,0,0,0,0,0,0,0,1,0,3,0,5,0,6,0,6,1,6,3,6,5,6,6,6,6,7,6,9,6,11,6,

%T 12,6,12,7,12,9,12,11,12,12,12,12,13,12,15,12,17,12,18,12,18,13,18,15,

%U 18,17,18,18,18,18,19,18,21,18,23,18,24,18,24,19,24,21,24,23,24,24,24

%N Number of n-digit cycles of length 5 under the Kaprekar map A151949

%H Joseph Myers, <a href="/A164736/b164736.txt">Table of n, a(n) for n=1..140</a>

%H <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>

%F Conjectures from _Chai Wah Wu_, Apr 13 2024: (Start)

%F a(n) = a(n-1) + a(n-2) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) + a(n-8) - a(n-9) for n > 15.

%F G.f.: x^11*(x^2 + 1)*(x^2 - x + 1)/((x - 1)^2*(x + 1)*(x^6 + x^3 + 1)). (End)

%Y Cf. A151949, A164727, A164728, A164731, A164732, A164733, A164734, A164735.

%K base,nonn

%O 1,13

%A _Joseph Myers_, Aug 23 2009