A360298 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A360298

Irregular triangle (an infinite binary tree) read by rows. The tree has root node 1 in row n = 1. For n > 1, each node with value m in row n-1 has a left child with value m / n if n divides m, and a right child with value m * n.

1, 2, 6, 24, 120, 20, 720, 140, 5040, 1120, 630, 40320, 10080, 70, 5670, 4480, 362880, 1008, 100800, 7, 700, 567, 56700, 448, 44800, 36288, 3628800, 11088, 1108800, 77, 7700, 6237, 623700, 4928, 492800, 399168, 39916800, 924, 133056, 92400, 13305600, 924, 92400, 74844, 51975, 7484400, 59136, 5913600, 33264, 4790016, 3326400, 479001600

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

OFFSET

1,2

COMMENTS

This sequence is a variant of A360173; here we use divisions and multiplications, there subtractions and additions.

The n-th row has A360299(n) terms, starts with A008336(n+1) and ends with A000142(n).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..11270 (rows for n = 1..26 flattened)

FORMULA

T(n, 1) = A008336(n+1).

T(n, A360299(n)) = A000142(n).

T(p, k) = p * T(p-1, k) for any prime number p.

EXAMPLE

The tree begins:

n n-th row

-- --------

1 1___

2 2___

3 6___

4 24___

5 _____________120_____________

| |

6 20___ 720___

| |

7 140___ _____5040_____

| | |

8 1120__ __630__ __40320__

| | | | |

9 10080 70 5670 4480 362880

PROG

(PARI) row(n) = { my (r = [1]); for (h = 2, n, r=concat(apply(v -> if (v%h==0, [v/h, v*h], [v*h]), r))); return (r) }

(Python)

from functools import cache

@cache

def row(n):

if n == 1: return [1]

out = []

for r in row(n-1): out += ([r//n] if r%n == 0 else []) + [r*n]

return out

print([an for r in range(1, 13) for an in row(r)]) # Michael S. Branicky, Feb 02 2023

CROSSREFS

Cf. A000142, A008336, A360173, A360299 (row lengths), A360300.

Sequence in context: A065422 A260850 A008336 * A033643 A050211 A248766

Adjacent sequences: A360295 A360296 A360297 * A360299 A360300 A360301

KEYWORD

nonn,look,tabf,easy

AUTHOR

Rémy Sigrist, Feb 02 2023

STATUS

approved