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A358468 Number of 2's that appeared by n-th step when constructing A030717.

%I A358468 #13 Nov 18 2022 10:13:49
%S A358468 0,0,1,2,3,3,3,3,4,6,8,9,10,11,12,14,16,19,23,26,27,29,32,38,43,48,51,
%T A358468 56,63,71,79,87,94,101,109,116,125,133,140,149,161,174,188,202,217,
%U A358468 233,250,266,284,304,326,347,369,392,418,444,471,499,530,561,593,625,658,692,726,761,797,833,869,906,944
%N A358468 Number of 2's that appeared by n-th step when constructing A030717.
%H A358468 Michael De Vlieger, <a href="/A358468/b358468.txt">Table of n, a(n) for n = 1..1024</a>
%H A358468 Michael De Vlieger, <a href="/A358468/a358468.png">Plot of the n-th row of A030717</a> n = 1..512, showing 2's in red and all other terms in blue.
%t A358468 nn = 94; c[_] = 0; k = a[1] = c[1] = 1; Accumulate@ Prepend[Reap[Do[w = Union@ Array[a, k]; t = 0; Do[Set[a[j + k], c[w[[j]]]]; If[a[j + k] == 2, t++], {j, Length[w]}]; Do[c[a[j + k]]++, {j, Length[w]}]; k += Length[w]; Sow[t], {n, nn}]][[-1, -1]], 0] (* _Michael De Vlieger_, Nov 18 2022 *)
%o A358468 (Ruby)
%o A358468 def A(k, n)
%o A358468   a = []
%o A358468   ary = [1]
%o A358468   n.times{
%o A358468     a << ary.count(k)
%o A358468     ary += ary.uniq.sort.map{|i| ary.count(i)}
%o A358468   }
%o A358468   a
%o A358468 end
%o A358468 p A(2, 100)
%Y A358468 Partial sums of A358469.
%Y A358468 Cf. A030717, A358466.
%K A358468 nonn
%O A358468 1,4
%A A358468 _Seiichi Manyama_, Nov 18 2022