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A204418 Periodic sequence 1,0,1,..., arranged in a triangle. 3
1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform is A130781.

Row sums: 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, ... = A004396(n+1) = A131737 (n+2) .

Diagonal sums: 1, 0, 2, 1, 1, 3, 3, 1, 5, 3, 2, 6, 5, 2, 8, 5, 3, 9, 7, 3, 11, 7, 4, 12, 9, 4, 14, 9, 5, 15, ..

Essentially the same as A141571 and A011655. - R. J. Mathar, Jan 16 2012

As sequence a(n) this is the characteristic sequence for the mod m reduced odd numbers (i.e., gcd(2*n+1,m)=1, n >= 0) for each modulus m from 3*A003586 = [3,6,9,12,18,24,27,36,48,...]. - Wolfdieter Lang, Feb 04 2012

Disregarding the triangle: a(A173732(n)) = 1. - Reinhard Zumkeller, Apr 29 2012

REFERENCES

Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

LINKS

Table of n, a(n) for n=0..71.

Index entries for linear recurrences with constant coefficients, signature (0,0,1).

FORMULA

If k==0 mod(3), T(n+k,k) = 1, 0, 1, 1, 0, 1, 1, 0, 1, ... (A204418)

If k==1 mod(3), T(n+k,k) = 1, 0, 0, 1, 0, 0, 1, 0, 0, ... (A079978)

If n==2 mod(3), T(n+k,k) = 1, 1, 1, 1, 1, 1, 1, 1, 1, ... (A000012)

a(A016777(n)) = 0.

G.f.:(1+x^2)/(1-x^3)

G.f.: U(0) where U(k)=  1 + x^2/(1 - x/(x + 1/U(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 17 2012

EXAMPLE

Triangle begins:

  1;

  0, 1;

  1, 0, 1;

  1, 0, 1, 1;

  0, 1, 1, 0, 1;

  1, 0, 1, 1, 0, 1;

  1, 0, 1, 1, 0, 1, 1;

  0, 1, 1, 0, 1, 1, 0, 1;

  1, 0, 1, 1, 0, 1, 1, 0, 1;

PROG

(PARI) a(n)=n%3!=1 \\ Charles R Greathouse IV, Jul 13 2016

CROSSREFS

Cf. A011655.

Sequence in context: A174208 A141687 A305385 * A260190 A260192 A057078

Adjacent sequences:  A204415 A204416 A204417 * A204419 A204420 A204421

KEYWORD

nonn,tabl,easy,changed

AUTHOR

Philippe Deléham, Jan 15 2012

STATUS

approved

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Last modified October 16 13:11 EDT 2019. Contains 328073 sequences. (Running on oeis4.)