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A293522
Number of bifurcating nodes at generation n in the binary tree of persistently squarefree numbers (see A293230).
5
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
0,3
COMMENTS
Bifurcating node is one that branches to two alive nodes in the next generation (level) of the tree.
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.
PROG
(PARI) \\ See program at A293520.
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2017
STATUS
approved