%I #7 Apr 13 2024 22:53:05
%S 0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,1,0,1,0,1,0,2,0,2,0,1,0,1,2,1,1,1,1,
%T 1,0,3,0,3,0,2,0,2,3,1,2,1,2,1,1,4,1,4,0,3,0,3,4,2,3,2,3,1,2,5,2,5,1,
%U 4,1,4,5,3,4,3,4,2,3,7,3,6,2,5,2,5,7,4,6,4,5,3,4,9,4,8,3,7,3,6,9,5,8,5,7,4
%N Number of n-digit cycles of length 2 under the Kaprekar map A151949
%H Joseph Myers, <a href="/A164734/b164734.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-7) + a(n-9) + a(n-14) - a(n-16) - a(n-21) - a(n-23) + a(n-30) for n > 41.
%F G.f.: x*(-x^40 - x^38 - x^36 + x^33 - x^32 + 2*x^31 - x^30 + 2*x^29 - x^28 + x^27 + x^25 - x^24 + 2*x^23 - x^22 + 2*x^21 - 2*x^20 + x^19 - x^16 - x^15 - x^14 + x^13 - x^12 + x^11 - x^4)/(x^30 - x^23 - x^21 - x^16 + x^14 + x^9 + x^7 - 1). (End)
%Y Cf. A151949, A164723, A164724, A164731, A164732, A164733, A164735, A164736.
%K base,nonn
%O 1,23
%A _Joseph Myers_, Aug 23 2009