A216607 The sequence used to represent partition binary diagram as an array.

0, 0, 1, 0, 1, 0, 2, 1, 0, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3

Offset: 1

Author

Mircea Merca, Sep 10 2012

Keywords

• nonn
• easy

Comments

This sequence differs from A025672 first at index n=110.

Links

• Mircea Merca, Binary Diagrams for Storing Ascending Compositions, Comp. J., 2012.

Crossrefs

Cf. A025672, A167268.

Programs

Maple

seq(floor((1/4)*ceil(sqrt(4*n))^2)-n,n=1..50)

PARI

A216607(n)=floor((1/4)*ceil(sqrt(4*n))^2)-n;

Formula

a(n) = floor((1/4)*ceiling(sqrt(4*n))^2) - n.

a(n^2) = a(n^2+n) = 0.

From Szymon Lukaszyk, Oct 27 2023: (Start)

a(n) = (-n) mod round(sqrt(n)).

a(n) = (A167268(n) - 2)/4. (End)