A304685 a(n) = A000699(n) (mod 3).

1, 1, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0

Offset

1,5

Comments

This is a 3-automatic sequence.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..2000

John M. Campbell, A DFA for enumerating even-order irreducible diagrams modulo 3

Index entries for 3-automatic sequences

Formula

For a natural number n, we have that a(n) = 1 if the ternary expansion of n is of the form 100...0 or is of the form 11...1200...0 for an even number of ones in this latter case, allowing runs of integers to be of length 0; a(n) = 2 if the ternary expansion of n is of the form 11...1200...0 if the length of the run of ones is odd; otherwise, a(n) = 0.

Example

We have that A000699(5) = 248, with 248 == 2 (mod 3), and the ternary expansion of 5 is given by the tuple (1, 2), so according to the above formula we have that a(5) = 2.

Maple

a:=proc(n) option remember; if n<=1 then 1; else
add((2*i-1)*procname(i)*procname(n-i), i=1..n-1) mod 3; end if; end proc:
seq(a(n), n=1..90); # Muniru A Asiru, Aug 15 2018

Prog

(PARI) a(n) = {my(A); A = O(x) ; for( i=1, n, A = x + A * (2 * x * A' - A)); polcoeff(A, n) % 3}; \\ Michel Marcus, Jul 04 2018; after A000699
(GAP) a:=[1];;  for n in [2..90] do a[n]:=(n-1)*Sum([1..n-1], i->a[i]*a[n-i]) mod 3; od; a; # Muniru A Asiru, Aug 15 2018

Crossrefs

Cf. A000699.

Sequence in context: A185644 A319080 A025435 * A186714 A160382 A336352

Adjacent sequences: A304682 A304683 A304684 * A304686 A304687 A304688

Keyword

nonn

Author

John M. Campbell, May 16 2018

Status

approved