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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. 3
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

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)