A331216 - OEIS

A331216

a(n) is the number of ways to write n = u + v where the binary representations of u and of v have the same number of 0's and the same number of 1's.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,12

COMMENTS

In other words, a(n) is the number of ways to write n as the sum of two binary anagrams.

Leading zeros are ignored.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Rémy Sigrist, PARI program for A331216

Rémy Sigrist, Scatterplot of (x, y) such that 0 <= x, y <= 2^10 and x and y are binary anagrams (a(n) corresponds to the number of pixels (x, y) such that x+y = n)

FORMULA

a(2*n) > 0.

a(2*n) >= a(n).

Apparently, a(3*2^k-1-x) = a(3*2^k-1+x) for any k >= 0 and x = -2^k..2^k.

EXAMPLE

For n = 22:

- we can write 22 as u + v in the following ways:

u v bin(u) bin(v)

-- -- ------ ------

10 12 1010 1100

11 11 1011 1011

12 10 1100 1010

- hence a(22) = 3.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A330827 (ternary analog), A331218 (decimal analog).

Sequence in context: A095774 A266874 A308343 * A071993 A317754 A317854

Adjacent sequences: A331213 A331214 A331215 * A331217 A331218 A331219

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 12 2020

STATUS

approved