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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.

%I A360298 #12 Feb 02 2023 14:41:03
%S A360298 1,2,6,24,120,20,720,140,5040,1120,630,40320,10080,70,5670,4480,
%T A360298 362880,1008,100800,7,700,567,56700,448,44800,36288,3628800,11088,
%U A360298 1108800,77,7700,6237,623700,4928,492800,399168,39916800,924,133056,92400,13305600,924,92400,74844,51975,7484400,59136,5913600,33264,4790016,3326400,479001600
%N 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.
%C A360298 This sequence is a variant of A360173; here we use divisions and multiplications, there subtractions and additions.
%C A360298 The n-th row has A360299(n) terms, starts with A008336(n+1) and ends with A000142(n).
%H A360298 Rémy Sigrist, <a href="/A360298/b360298.txt">Table of n, a(n) for n = 1..11270</a> (rows for n = 1..26 flattened)
%F A360298 T(n, 1) = A008336(n+1).
%F A360298 T(n, A360299(n)) = A000142(n).
%F A360298 T(p, k) = p * T(p-1, k) for any prime number p.
%e A360298 The tree begins:
%e A360298   n     n-th row
%e A360298   --    --------
%e A360298    1    1___
%e A360298             |
%e A360298    2        2___
%e A360298                 |
%e A360298    3            6___
%e A360298                     |
%e A360298    4               24___
%e A360298                         |
%e A360298    5      _____________120_____________
%e A360298          |                             |
%e A360298    6    20___                         720___
%e A360298              |                              |
%e A360298    7        140___                   _____5040_____
%e A360298                   |                 |              |
%e A360298    8            1120__           __630__       __40320__
%e A360298                       |         |       |     |         |
%e A360298    9                10080      70     5670  4480     362880
%o A360298 (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) }
%o A360298 (Python)
%o A360298 from functools import cache
%o A360298 @cache
%o A360298 def row(n):
%o A360298     if n == 1: return [1]
%o A360298     out = []
%o A360298     for r in row(n-1): out += ([r//n] if r%n == 0 else []) + [r*n]
%o A360298     return out
%o A360298 print([an for r in range(1, 13) for an in row(r)]) # _Michael S. Branicky_, Feb 02 2023
%Y A360298 Cf. A000142, A008336, A360173, A360299 (row lengths), A360300.
%K A360298 nonn,look,tabf,easy
%O A360298 1,2
%A A360298 _Rémy Sigrist_, Feb 02 2023