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

Offset: 0

Author

Antti Karttunen, Oct 12 2017

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A293230, A293441, A293520, A293521.

Programs

PARI

\\ See program at A293520.

Formula

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

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