A352502 a(n) is the number of integers k in the interval 0..n such that k and n-k can be added without carries in balanced ternary.

1, 2, 2, 4, 4, 2, 4, 4, 6, 10, 8, 6, 10, 8, 2, 4, 4, 6, 10, 8, 6, 10, 8, 10, 16, 12, 18, 28, 20, 14, 22, 16, 10, 16, 12, 18, 28, 20, 14, 22, 16, 2, 4, 4, 6, 10, 8, 6, 10, 8, 10, 16, 12, 18, 28, 20, 14, 22, 16, 10, 16, 12, 18, 28, 20, 14, 22, 16, 18, 28, 20, 30

Offset

0,2

Comments

Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.

This sequence has connections with Gould's sequence (A001316); here we work with balanced ternary, there with binary.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Wikipedia, Balanced ternary

Formula

a(n) <= n+1 with equality iff n belongs to A140429.

a(3*n) = 3*a(n) - 2.

a(3*n+1) = a(3*n-1) + 2.

Example

For n = 8:
- we consider the following cases:
              k|    0    1    2    3    4    5    6    7    8
      ---------+---------------------------------------------
        bter(k)|    0    1   1T   10   11  1TT  1T0  1T1  10T
      bter(8-k)|  10T  1T1  1T0  1TT   11   10   1T    1    0
       carries?|  no   yes  no   no   yes  no   no   yes  no
- so a(8) = 6.

Prog

(PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) }
a(n) = sum(k=0, n, ok(n-k, k))

Crossrefs

Cf. A001316, A059095, A140429, A353174 (corresponding k's).

Sequence in context: A368558 A060267 A214516 * A238004 A048244 A056673

Adjacent sequences: A352499 A352500 A352501 * A352503 A352504 A352505

Keyword

nonn,base

Author

Rémy Sigrist, Apr 28 2022

Status

approved