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%I #50 Nov 28 2021 12:33:59
%S 0,1,0,1,2,0,3,7,0,12,0,30,85,0,173,476,0,961,0,2652,8045,0,17637,
%T 51033,0,108950,312455,0,663535,0
%N a(n) is the number of odd numbers k < 2^n such that A260590(k) = n.
%C a(n) is either 0 or about c^(n-1) with c = log(3)/log(2).
%C Out of the first thirty terms, 12, or 40% are zeros.
%C Nonzero values give A100982. - _Ruud H.G. van Tol_, Nov 25 2021
%C A close variant of this sequence, that starts at offset 0, but with a(0)=0 and a(1)=1, maps it to the count of dropping patterns of 2^n+c(2^n), with the c(2^n) as mentioned with A177789. The positions of the zeros of that variant sequence might be a close variant of A054414, again with a(0)=0 (not properly checked yet). - _Ruud H.G. van Tol_, Nov 28 2021
%e a(1) = 0 since there exists no odd number whose msa is 1;
%e a(2) = 1 since there is only one odd number, 5 with k=2 2k+1, with k less than 2^2 whose msa is 2;
%e a(3) = 0 since there exists no odd number whose msa is 3;
%e a(4) = 1 since there is only one number, 1, less than 2^(4+1) whose msa is 4;
%e a(5) = 2 since there are two numbers, 11 & 23, less than 2^(4+1) whose msa is 4; etc.
%t msa[n_] := If[ OddQ@ n, (3n + 1)/2, n/2]; f[n_] := Block[{k = 2n + 1}, Length@ NestWhileList[ msa@# &, k, # >= k &] - 1]; g[n_] := Length@ Select[ Range[ 2^(n - 1)], f@# == n &]; Array[ g, 20]
%Y Cf. A260590, A054414, A100982, A186009, A186008, A177789.
%K nonn,more
%O 1,5
%A Joseph K. Horn, O. Praem, and _Robert G. Wilson v_, Jul 29 2015
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