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A381587 a(1) = 1; thereafter the sequence is extended by iteratively appending the run length transform of the reverse of the sequence thus far.

%I A381587 #31 Mar 04 2025 07:35:18
%S A381587 1,1,2,1,2,1,1,1,2,1,3,1,1,1,2,1,3,1,1,1,3,1,1,1,2,1,3,1,3,1,1,1,3,1,
%T A381587 1,1,3,1,1,1,2,1,3,1,3,1,3,1,1,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2,1,
%U A381587 3,1,3,1,3,1,1,1,5,1,1,1,1,1,1,1,3,1,3
%N A381587 a(1) = 1; thereafter the sequence is extended by iteratively appending the run length transform of the reverse of the sequence thus far.
%C A381587 The run length transform replaces each run of consecutive equal values with a single value representing the length of that run.
%C A381587 Is 2 the greatest even number in the sequence?
%C A381587 It appears that the limit of the rows read in reverse equals A306346 (ignoring the initial terms). - _Paul D. Hanna_, Mar 03 2025
%H A381587 Paul D. Hanna, <a href="/A381587/b381587.txt">Table of n, a(n) for n = 1..9259 (first 20 rows)</a>
%e A381587 Irregular triangle begins:
%e A381587   1;
%e A381587   1;
%e A381587   2;
%e A381587   1,2;
%e A381587   1,1,1,2;
%e A381587   1,3,1,1,1,2;
%e A381587   1,3,1,1,1,3,1,1,1,2;
%e A381587   1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2;
%e A381587   1,3,1,3,1,3,1,1,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2;
%e A381587   ...
%o A381587 (PARI) \\ From _Paul D. Hanna_, Mar 03 2025: (Start)
%o A381587 \\ RUNS(V) Returns vector of run lengths in vector V:
%o A381587 {RUNS(V) = my(R=[],c=1);if(#V>1, for(n=2,#V, if(V[n]==V[n-1], c=c+1, R=concat(R,c); c=1))); R=concat(R,c)}
%o A381587 \\ REV(V) Reverses order of vector V:
%o A381587 {REV(V) = Vec(Polrev(Ser(V)))}
%o A381587 \\ Generates N rows as a vector A of row vectors
%o A381587 {N=15; A=vector(N);A[1]=[1];A[2]=[1];A[3]=[2];
%o A381587 for(n=3,#A-1, A[n+1] = concat(RUNS(REV(A[n])),A[n]);); A}
%o A381587 for(n=1,N,print(A[n])) \\ Print N rows of this triangle (End)
%Y A381587 Cf. A381357 (row lengths), A381358 (row sums), A381356 (limit of rows), A306346.
%Y A381587 Cf. A306211.
%K A381587 tabf,nonn
%O A381587 1,3
%A A381587 _Neal Gersh Tolunsky_, Feb 27 2025