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 A232089 #31 Nov 28 2024 13:29:42
%S A232089 1,1,1,1,1,2,1,1,2,4,1,1,2,4,8,1,1,2,4,8,16,1,1,2,4,8,16,32,1,1,2,4,8,
%T A232089 16,32,64,1,1,2,4,8,16,32,64,128,1,1,2,4,8,16,32,64,128,256,1,1,2,4,8,
%U A232089 16,32,64,128,256,512
%N A232089 Table read by rows, which consist of 1 followed by 2^k, 0 <= k < n ; n = 0,1,2,3,...
%C A232089 The n-th row consists of the n+1 terms A011782(k), k=0,...,n. Thus the rows converge to A011782, which is also equal to the diagonal = last element of each row.
%C A232089 This (read as a "linear" sequence) is also the limit of the rows of A232088; more precisely, for n>0, each row of A232088 consists of the first n(n+1)/2 elements of this sequence, followed by 2^(n-1). See the LINK there for one motivation for this sequence.
%H A232089 Harvey P. Dale, <a href="/A232089/b232089.txt">Table of n, a(n) for n = 0..1000</a>
%F A232089 T(n,k) = max(1,2^(k-1)) = A011782(k); 0 <= k <= n.
%e A232089 The table reads:
%e A232089 1,
%e A232089 1, 1,
%e A232089 1, 1, 2,
%e A232089 1, 1, 2, 4,
%e A232089 1, 1, 2, 4, 8,
%e A232089 1, 1, 2, 4, 8, 16,
%e A232089 1, 1, 2, 4, 8, 16, 32,
%e A232089 1, 1, 2, 4, 8, 16, 32, 64, etc.
%t A232089 Join[{1},Flatten[Table[Join[{1},2^Range[0,n]],{n,0,10}]]] (* _Harvey P. Dale_, Nov 28 2024 *)
%o A232089 (PARI) for(n=0,10,print1("1,");for(k=0,n-1,print1(2^k,",")))
%K A232089 nonn,tabl,easy
%O A232089 0,6
%A A232089 _M. F. Hasler_, Jan 20 2014