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).

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, 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, 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

Offset: 1

Author

Rémy Sigrist, May 01 2021

Keywords

• nonn
• tabf

Comments

Sequence A061419 and A343857 gives row lengths and partial sums, respectively.

The n-th row sums to 2^(n-1).

This sequence has fractal features.

As with Jim Conant's iterative dissection of a square (A328078), at each iteration, we split in two odd-indexed elements.

This sequence has similarities with A205592: in A205592:

- we start with A205592(1) = 1,

- for k = 1, 2, ...:

if k is odd: append two copies of A205592(k),

if k is even: append 2*A205592(k).

Examples

			Table begins:
1:  [1]
2:  [1, 1]
3:  [1, 1, 2]
4:  [1, 1, 2, 2, 2]
5:  [1, 1, 2, 2, 2, 4, 2, 2]
6:  [1, 1, 2, 2, 2, 4, 2, 2, 8, 2, 2, 4]
7:  [1, 1, 2, 2, 2, 4, 2, 2, 8, 2, 2, 4, 8, 8, 4, 2, 2, 8]
		

Crossrefs

Cf. A061419, A205592, A328078, A343857.

Programs

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) }

Python

def auptorow(rows):
  alst, row, newrow = [1], [1], []
  for r in range(2, rows+1):
    for i, v in enumerate(row, start=1): newrow += [v, v] if i%2 else [2*v]
    alst, row, newrow = alst + newrow, newrow, []
  return alst
print(auptorow(9)) # Michael S. Branicky, May 04 2021