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%I #10 Apr 13 2024 22:52:57
%S 1,0,1,1,0,2,0,2,2,3,1,5,1,6,2,8,2,12,3,14,5,17,7,21,8,25,12,30,14,36,
%T 17,43,21,49,25,58,31,66,36,75,43,85,49,96,58,109,66,121,75,136,86,
%U 150,96,167,109,184,121,202,136,222,150,242,167,265,185,287,202,313,222,338
%N Number of n-digit fixed points under the Kaprekar map A151949
%H Joseph Myers, <a href="/A164733/b164733.txt">Table of n, a(n) for n=1..70</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-2) + a(n-6) - a(n-8) + a(n-9) - a(n-11) + a(n-14) - a(n-15) - a(n-16) + a(n-17) - a(n-20) + a(n-22) - a(n-23) + a(n-25) + a(n-29) - a(n-31) for n > 33.
%F G.f.: x*(-x^32 + x^31 - x^29 + x^28 - x^27 + x^26 - x^24 + 2*x^23 - x^22 + x^21 + x^20 + 2*x^18 - x^17 + x^16 + 2*x^15 - 3*x^14 + 2*x^13 - x^12 + x^11 - x^9 + 2*x^8 - x^6 + x^5 - x^4 + x^3 + 1)/(x^31 - x^29 - x^25 + x^23 - x^22 + x^20 - x^17 + x^16 + x^15 - x^14 + x^11 - x^9 + x^8 - x^6 - x^2 + 1). (End)
%Y Cf. A151949, A099009, A164731, A164732, A164734, A164735, A164736.
%Y Bisections: A309223, A309224.
%Y In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9). [From _Joseph Myers_, Sep 05 2009]
%K base,nonn
%O 1,6
%A _Joseph Myers_, Aug 23 2009