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 A089606 #15 Feb 24 2023 18:29:53 %S A089606 1,2,1,4,2,1,8,3,2,1,16,5,3,2,1,32,7,4,3,2,1,64,10,6,4,3,2,1,128,13,8, %T A089606 5,4,3,2,1,256,18,10,7,5,4,3,2,1,512,23,13,9,6,5,4,3,2,1,1024,30,16, %U A089606 11,8,6,5,4,3,2,1,2048,37,19,13,10,7,6,5,4,3,2,1 %N A089606 Table T(n,k), n>=1 and k>=1; the k-th row is defined by :partial sums of the sequence 1, a(1), .., a(1), a(2), .., a(2), a(3), ..,a(3), a(4), ... each term repeated k times (with a(i)= T(i,k)). %C A089606 Row k=1 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, ... %C A089606 Row k=2 : 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, ... %C A089606 Row k=3 : 1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 27, ... %C A089606 Row k=4 : 1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 19, 22, ... %C A089606 Row k=5 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 19, ... %H A089606 Alois P. Heinz, <a href="/A089606/b089606.txt">First 200 antidiagonals, flattened</a> %F A089606 T(n,1) = A000079(n-1) = 2^(n-1). %F A089606 T(n,2) = A033485(n). %F A089606 T(n,3) = A089649(n). %F A089606 T(n,4) = A089651(n). %p A089606 T:= proc(n, k) option remember; `if`(n=1, 1, %p A089606 T(n-1, k)+T(floor((n+k-2)/k), k)) %p A089606 end: %p A089606 seq(seq(T(1+d-k,k), k=1..d), d=1..12); # _Alois P. Heinz_, Feb 24 2023 %Y A089606 Cf. A000079, A033485, A089649, A089651. %K A089606 easy,nonn,tabl %O A089606 1,2 %A A089606 _Philippe Deléham_, Jan 03 2004