This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381357 #17 Mar 03 2025 13:02:45
%S A381357 1,1,1,2,4,6,10,16,26,42,66,102,156,238,364,560,868,1354,2120,3322,
%T A381357 5198,8112,12624,19602,30400,47138,73138,113598,176630,274858
%N A381357 Row lengths of irregular triangle A381587.
%C A381357 If it exists, what is the limit of a(n)^(1/n) as n increases?
%e A381357 Row n+1 of irregular triangle A381587 equals the run lengths of the first n rows of the triangle (flattened) when read in reverse order, starting with
%e A381357 1;
%e A381357 1;
%e A381357 2;
%e A381357 1,2;
%e A381357 1,1,1,2;
%e A381357 1,3,1,1,1,2;
%e A381357 1,3,1,1,1,3,1,1,1,2;
%e A381357 1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2; ...
%e A381357 This sequence gives the row lengths [1, 1, 1, 2, 4, 6, 10, 16, ...].
%o A381357 (PARI) \\ Print the row lengths of irregular triangle A381587
%o A381357 \\ RUNS(V) Returns vector of run lengths in vector V:
%o A381357 {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 A381357 \\ REV(V) Reverses order of vector V:
%o A381357 {REV(V) = Vec(Polrev(Ser(V)))}
%o A381357 \\ Generates N rows as a vector A of row vectors
%o A381357 {N=25; A=vector(N); A[1]=[1]; A[2]=[1]; A[3]=[2];
%o A381357 for(n=3, #A-1, A[n+1] = concat(RUNS(REV(A[n])), A[n]); );}
%o A381357 \\ Print the row lengths of the first N rows
%o A381357 for(n=1, N, print1(#A[n],", "))
%Y A381357 Cf. A381587, A381358.
%K A381357 nonn,more
%O A381357 1,4
%A A381357 _Paul D. Hanna_, Mar 03 2025