cp's OEIS Frontend

A343856 Irregular table read by rows; the first row is [1]; to obtain the next row, replace each odd-indexed term u with (u, u), and each even-indexed term v with (2*v).

%I A343856 #13 Mar 30 2024 23:08:07
%S A343856 1,1,1,1,1,2,1,1,2,2,2,1,1,2,2,2,4,2,2,1,1,2,2,2,4,2,2,8,2,2,4,1,1,2,
%T A343856 2,2,4,2,2,8,2,2,4,8,8,4,2,2,8,1,1,2,2,2,4,2,2,8,2,2,4,8,8,4,2,2,8,8,
%U A343856 8,16,4,4,4,2,2,16,1,1,2,2,2,4,2,2,8,2,2,4,8,8,4,2,2,8,8,8,16,4,4,4,2,2,16,8,8,16,16,16,8,4,4,8,2,2,4,16,16
%N A343856 Irregular table read by rows; the first row is [1]; to obtain the next row, replace each odd-indexed term u with (u, u), and each even-indexed term v with (2*v).
%C A343856 Sequence A061419 and A343857 gives row lengths and partial sums, respectively.
%C A343856 The n-th row sums to 2^(n-1).
%C A343856 This sequence has fractal features.
%C A343856 As with Jim Conant's iterative dissection of a square (A328078), at each iteration, we split in two odd-indexed elements.
%C A343856 This sequence has similarities with A205592: in A205592:
%C A343856 - we start with A205592(1) = 1,
%C A343856 - for k = 1, 2, ...:
%C A343856     if k is odd: append two copies of A205592(k),
%C A343856     if k is even: append 2*A205592(k).
%e A343856 Table begins:
%e A343856 1:  [1]
%e A343856 2:  [1, 1]
%e A343856 3:  [1, 1, 2]
%e A343856 4:  [1, 1, 2, 2, 2]
%e A343856 5:  [1, 1, 2, 2, 2, 4, 2, 2]
%e A343856 6:  [1, 1, 2, 2, 2, 4, 2, 2, 8, 2, 2, 4]
%e A343856 7:  [1, 1, 2, 2, 2, 4, 2, 2, 8, 2, 2, 4, 8, 8, 4, 2, 2, 8]
%o A343856 (PARI) { a = r = [1]; for (n=1, 8, i = 0; a=concat(a, r = concat(apply (v -> if (i++%2, [v,v], [2*v]), r)))); print (a) }
%o A343856 (Python)
%o A343856 def auptorow(rows):
%o A343856   alst, row, newrow = [1], [1], []
%o A343856   for r in range(2, rows+1):
%o A343856     for i, v in enumerate(row, start=1): newrow += [v, v] if i%2 else [2*v]
%o A343856     alst, row, newrow = alst + newrow, newrow, []
%o A343856   return alst
%o A343856 print(auptorow(9)) # _Michael S. Branicky_, May 04 2021
%Y A343856 Cf. A061419, A205592, A328078, A343857.
%K A343856 nonn,tabf
%O A343856 1,6
%A A343856 _Rémy Sigrist_, May 01 2021