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A369305 Number of terms in A343524 that are less than 10^n.

%I A369305 #41 Jun 15 2024 18:35:35
%S A369305 1,10,19,55,91,175,259,385,511,637,763,847,931,967,1003,1012,1021,
%T A369305 1022,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,
%U A369305 1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023,1023
%N A369305 Number of terms in A343524 that are less than 10^n.
%C A369305 The tallied terms (A343524) are palindromes with digits strictly increasing up to the midpoint.
%H A369305 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A369305 a(n) = 1023 for n >= 18. - _Michael S. Branicky_, Jan 22 2024
%F A369305 a(n) = Sum_{k=1..n+1} binomial(9,floor(k/2)). - _Andrew Howroyd_, Jan 22 2024
%F A369305 G.f.: (-x^18 - x^17 - 9*x^16 - 9*x^15 - 36*x^14 - 36*x^13 - 84*x^12 - 84*x^11 - 126*x^10 - 126*x^9 - 126*x^8 - 126*x^7 - 84*x^6 - 84*x^5 - 36*x^4 - 36*x^3 - 9*x^2 - 9*x - 1)/(x - 1). - _Chai Wah Wu_, Jun 15 2024
%e A369305 For n = 0, 10^0 = 1, there is a single A343524 term less than 1: 0.
%e A369305 For n = 2, 10^2 = 100, there are 19 A343524 terms less than 100: 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99.
%e A369305 Examples of A343524 terms less than 100000: 1661, 28982.
%o A369305 (PARI) a(n)=sum(k=1, min(n,18)+1, binomial(9,k\2)) \\ _Andrew Howroyd_, Jan 22 2024
%o A369305 (Python)
%o A369305 from math import comb
%o A369305 def a(n):
%o A369305     if n > 18: return 1023
%o A369305     return 1+sum(comb(9, (digits+1)//2) for digits in range(1, n+1))
%o A369305 print([a(n) for n in range(47)]) # _Michael S. Branicky_, Jan 22 2024
%Y A369305 Cf. A134941, A173070, A343524.
%K A369305 nonn,base,easy
%O A369305 0,2
%A A369305 _James S. DeArmon_, Jan 19 2024
%E A369305 a(11) and beyond from _Michael S. Branicky_, Jan 22 2024