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

1,7

Comments

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

Links

Table of n, a(n) for n=1..87.

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

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)

Maple

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

Prog

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

Crossrefs

Cf. A025672, A167268.

Sequence in context: A128313 A283486 A330759 * A025672 A025665 A357022

Adjacent sequences: A216604 A216605 A216606 * A216608 A216609 A216610

Keyword

nonn,easy

Author

Mircea Merca, Sep 10 2012

Status

approved