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A117908 Chequered triangle for odd prime p=3. 2
1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are A117909. Diagonal sums are A117910. For odd prime p, T(n,k;p)=[k<=n]*0^abs(L(C(n,p-1)/p)-2*L(C(k,p-1)/p)) defines a chequered triangle for p.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

G.f.: (1+x(1+y)+x^3*y)/((1-x^3)(1-x^3*y^3)); Number triangle T(n,k)=[k<=n]*0^abs(L(C(n,2)/3)-2*L(C(k,2)/3)) where L(j/p) is the Legendre symbol of j and p.

EXAMPLE

Triangle begins

1,

1, 1,

0, 0, 0,

1, 1, 0, 1,

1, 1, 0, 1, 1,

0, 0, 0, 0, 0, 0,

1, 1, 0, 1, 1, 0, 1,

1, 1, 0, 1, 1, 0, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0,

1, 1, 0, 1, 1, 0, 1, 1, 0, 1,

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1,

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

CROSSREFS

Cf. A117904.

Sequence in context: A143466 A195053 A267136 * A115360 A088911 A179763

Adjacent sequences:  A117905 A117906 A117907 * A117909 A117910 A117911

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Apr 01 2006

STATUS

approved

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Last modified January 20 23:24 EST 2020. Contains 331104 sequences. (Running on oeis4.)