A293522 - OEIS

A293522

Number of bifurcating nodes at generation n in the binary tree of persistently squarefree numbers (see A293230).

1, 1, 2, 2, 3, 5, 5, 5, 9, 12, 17, 21, 27, 36, 50, 64, 89, 114, 156, 201, 261, 353, 480, 639, 870, 1163, 1562, 2116, 2826, 3798, 5080, 6884, 9176, 12329, 16627, 22262, 29980, 40421, 54126, 72642, 97877, 131266, 176638, 237227, 318659, 427624, 574993, 772511, 1038418, 1395802

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OFFSET

0,3

COMMENTS

Bifurcating node is one that branches to two alive nodes in the next generation (level) of the tree.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

a(n) = Sum_{k=(2^n)..(2^(1+n))-1)] abs(A293233(k)) * A008966(2k) * A008966(1+2k).

a(n) <= A293441(n). [Because no even node can bifurcate.]

EXAMPLE

a(2) = 2 because in the binary tree illustrated in A293230, there are two nodes at the level 2 (namely 5 and 7) that spawn two offspring each.