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Search: id:A117908
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| A117908 |
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Chequered triangle for odd prime p=3. |
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+0
3
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| 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; listen)
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OFFSET
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0,1
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COMMENT
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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.
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FORMULA
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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.
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EXAMPLE
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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
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CROSSREFS
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Cf. A117904.
Sequence in context: A127001 A068431 A143466 this_sequence A115360 A088911 A105349
Adjacent sequences: A117905 A117906 A117907 this_sequence A117909 A117910 A117911
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 01 2006
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