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

0,7

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.

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)

Example

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.

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A365401 A212181 A256452 * A010276 A214268 A214249

Adjacent sequences: A330824 A330825 A330826 * A330828 A330829 A330830

Keyword

nonn,base

Author

Rémy Sigrist, Jan 12 2020

Status

approved