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A358985 a(n) is the number of numbers of the form k + reverse(k) for at least one n-digit number k.

%I A358985 #26 Oct 04 2024 10:02:18
%S A358985 10,18,180,342,3420,6498,64980,123462,1234620,2345778,23457780,
%T A358985 44569782,445697820,846825858,8468258580,16089691302,160896913020,
%U A358985 305704134738,3057041347380,5808378560022,58083785600220,110359192640418,1103591926404180,2096824660167942
%N A358985 a(n) is the number of numbers of the form k + reverse(k) for at least one n-digit number k.
%H A358985 Paolo Xausa, <a href="/A358985/b358985.txt">Table of n, a(n) for n = 1..1000</a>
%H A358985 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,19).
%F A358985 a(2n+1) = 10*a(2n) for n > 0. - _Chai Wah Wu_, Dec 09 2022
%F A358985 a(2n) = 19*a(2n-2) for n > 1. - _Robert G. Wilson v_, Dec 10 2022
%F A358985 a(n) = 19*a(n-2). - _Wesley Ivan Hurt_, Mar 17 2023
%e A358985 There are 10 numbers of the form k + reverse(k) for 1-digit numbers k: 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18, so a(1) = 10.
%e A358985 There are 18 numbers of the form k + reverse(k) for 2-digit numbers k: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, and 198, so a(2) = 18.
%t A358985 LinearRecurrence[{0, 19}, {10, 18, 180}, 30] (* _Paolo Xausa_, Oct 04 2024 *)
%o A358985 (Python)
%o A358985 def A358985(n):
%o A358985     if n == 1:
%o A358985         return 10
%o A358985     kset = set()
%o A358985     for i in range(10**(n-2),10**(n-1)):
%o A358985         for j in range(int((s:=str(i))[0])+1):
%o A358985             kset.add(10*i+j+int(str(j)+s[::-1]))
%o A358985     return len(kset) # _Chai Wah Wu_, Dec 09 2022
%o A358985 (PARI) a(n) = (18+(n<2))*19^(n\2-1)*10^(n%2); \\ _Jinyuan Wang_, Dec 14 2022
%Y A358985 Cf. A067030, A358986.
%K A358985 nonn,base
%O A358985 1,1
%A A358985 _Jon E. Schoenfield_, Dec 08 2022
%E A358985 More terms from _Jinyuan Wang_, Dec 14 2022