A330827 a(n) is the numbers of ways to write 2*n = u + v where the ternary representations of u and of v have the same number of digits d for d = 0..2.

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 5, 3, 3, 5, 3, 5, 3, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 5, 3, 5, 3, 5, 5, 5, 7, 5, 7, 7, 5, 9, 7, 7, 11, 7, 9, 7, 7, 7, 11, 9, 13, 5, 9, 5, 15, 7, 9, 7, 7, 7, 7, 7, 5, 5, 5, 3, 5, 3, 5, 3, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3

Offset: 0

Author

Rémy Sigrist, Jan 12 2020

Keywords

• nonn
• base

Comments

In other words, a(n) is the number of ways to write 2*n as the sum of two ternary anagrams.

Leading zeros are ignored.

Two ternary anagrams have necessarily the same parity, hence an odd number cannot be the sum of two ternary anagrams.

Examples

			For n = 6:
- we can write 12 as u + v in the following ways:
  u  v  ter(u)  ter(v)
  -  -  ------  ------
  5  7      12      21
  6  6      20      20
  7  5      21      12
- hence a(6) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..19683
• Rémy Sigrist, PARI program for A330827
• Rémy Sigrist, Scatterplot of (x, y) such that 0 <= x, y <= 3^7 and x and y are ternary anagrams (a(n) corresponds to the number of pixels (x, y) such that x+y = n)

Crossrefs

Cf. A331216 (binary analog), A331218 (decimal analog).

Programs

PARI

See Links section.