A293521 - OEIS

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A293521

Number of surviving (but not bifurcating) nodes at generation n in the binary tree of persistently squarefree numbers (see A293230).

0, 1, 1, 3, 3, 2, 5, 9, 8, 11, 15, 24, 30, 42, 51, 76, 94, 126, 158, 217, 298, 403, 539, 731, 970, 1305, 1748, 2322, 3179, 4225, 5715, 7596, 10259, 13731, 18357, 24771, 33184, 44448, 59968, 80764, 107973, 145638, 195237, 262446, 352904, 474964, 637081, 856232, 1149966, 1543986, 2076534, 2789516

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..51.

FORMULA

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

a(n) = A293518(n) + A293519(n). [even survivors + odd survivors.]

EXAMPLE

a(2) = 1 because in the binary tree illustrated in A293230, there is only one node at the level (namely, the node 6) that spawns just one offspring.

PROG

(PARI) \\ See program at A293520.