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 A381358 #16 Mar 03 2025 13:02:40
%S A381358 1,1,2,3,5,9,15,25,41,67,109,175,277,433,671,1035,1595,2463,3817,5937,
%T A381358 9259,14457,22569,35193,54795,85195,132333,205471,319069,495699
%N A381358 Row sums of irregular triangle A381587.
%C A381358 If it exists, what is the limit of a(n)^(1/n) as n increases?
%e A381358 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 A381358 1;
%e A381358 1;
%e A381358 2;
%e A381358 1,2;
%e A381358 1,1,1,2;
%e A381358 1,3,1,1,1,2;
%e A381358 1,3,1,1,1,3,1,1,1,2;
%e A381358 1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2; ...
%e A381358 This sequence gives the row sums [1, 1, 2, 3, 5, 9, 15, 25, ...].
%o A381358 (PARI) \\ Print the row sums of irregular triangle A381587
%o A381358 \\ RUNS(V) Returns vector of run lengths in vector V:
%o A381358 {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 A381358 \\ REV(V) Reverses order of vector V:
%o A381358 {REV(V) = Vec(Polrev(Ser(V)))}
%o A381358 \\ Generates N rows as a vector A of row vectors
%o A381358 {N=25; A=vector(N); A[1]=[1]; A[2]=[1]; A[3]=[2];
%o A381358 for(n=3, #A-1, A[n+1] = concat(RUNS(REV(A[n])), A[n]); );}
%o A381358 \\ Print the row sums of the first N rows
%o A381358 for(n=1, N, print1(vecsum(A[n]),", "))
%Y A381358 Cf. A381587, A381357.
%K A381358 nonn,more
%O A381358 1,3
%A A381358 _Paul D. Hanna_, Mar 03 2025