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

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.

Crossrefs

Cf. A293230, A293441, A293518, A293519, A293520, A293522.

Sequence in context: A186111 A186813 A329690 * A285443 A110898 A264756

Adjacent sequences: A293518 A293519 A293520 * A293522 A293523 A293524

Keyword

nonn

Author

Antti Karttunen, Oct 12 2017

Status

approved