A164733 Number of n-digit fixed points under the Kaprekar map A151949.
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, 17, 43, 21, 49, 25, 58, 31, 66, 36, 75, 43, 85, 49, 96, 58, 109, 66, 121, 75, 136, 86, 150, 96, 167, 109, 184, 121, 202, 136, 222, 150, 242, 167, 265, 185, 287, 202, 313, 222, 338
Offset: 1
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Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
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.
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)
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