OFFSET
0,3
COMMENTS
Notation: (3)[n](-1).
Fixed point of the morphism 0 -> 0,1,2; 1 -> -1,0,1; 2 -> -2,-1,0; ...; n -> -n,-n+1,-n+2. - Philippe Deléham, Oct 22 2011
FORMULA
a(n) = Sum_{k>=0} A030341(n,k)*(-1)^k. - Philippe Deléham, Oct 22 2011.
G.f. A(x) satisfies: A(x) = x * (1 + 2*x) / (1 - x^3) - (1 + x + x^2) * A(x^3). - Ilya Gutkovskiy, Jul 28 2021
EXAMPLE
15 = +1(9)+2(3)+0(1) -> +1(+1)+2(-1)+0(+1) = -1 = a(15).
PROG
(Python)
from sympy.ntheory.digits import digits
def a(n):
return sum(bi*(-1)**k for k, bi in enumerate(digits(n, 3)[1:][::-1]))
print([a(n) for n in range(104)]) # Michael S. Branicky, Jul 28 2021
(Python)
from sympy.ntheory import digits
def A065368(n): return sum((0, 1, 2, -1, 0, 1, -2, -1, 0)[i] for i in digits(n, 9)[1:]) # Chai Wah Wu, Jul 19 2024
CROSSREFS
KEYWORD
base,easy,sign
AUTHOR
Marc LeBrun, Oct 31 2001
EXTENSIONS
Initial 0 added by Philippe Deléham, Oct 22 2011
STATUS
approved