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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
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, 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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 12 2020
STATUS
approved