

A304685


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


1



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
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OFFSET

1,5


COMMENTS

This is a 3automatic sequence.


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..2000
John M. Campbell, A DFA for enumerating evenorder irreducible diagrams modulo 3
Index entries for 3automatic 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*i1)*procname(i)*procname(ni), i=1..n1) 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]:=(n1)*Sum([1..n1], i>a[i]*a[ni]) mod 3; od; a; # Muniru A Asiru, Aug 15 2018


CROSSREFS

Cf. A000699.
Sequence in context: A185644 A319080 A025435 * A186714 A160382 A081221
Adjacent sequences: A304682 A304683 A304684 * A304686 A304687 A304688


KEYWORD

nonn


AUTHOR

John M. Campbell, May 16 2018


STATUS

approved



