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

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

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Apr 28 2022

STATUS

approved