A343856 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

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).

LINKS

Table of n, a(n) for n=1..117.

EXAMPLE

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]

PROG

(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

CROSSREFS

Cf. A061419, A205592, A328078, A343857.

Sequence in context: A223708 A060778 A096492 * A053874 A170906 A123245

Adjacent sequences: A343853 A343854 A343855 * A343857 A343858 A343859

KEYWORD

nonn,tabf

AUTHOR

Rémy Sigrist, May 01 2021

STATUS

approved