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A304685
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a(n) = A000699(n) (mod 3).
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1
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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
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1,5
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COMMENTS
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This is a 3-automatic sequence.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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MAPLE
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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:
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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