A117567 Riordan array ((1+x^2)/(1-x^3),x).

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

Offset

0,1

Comments

Sequence array for the sequence F(L((n+2)/3)). Row sums are A093878. Diagonal sums are A051275. Inverse is A117568.

References

Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

Links

Table of n, a(n) for n=0..90.

D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.

Formula

Number triangle T(n,k)=F(L((n-k+2)/3))[k<=n] where L(j/p) is the Legendre symbol of j and p.

Example

Triangle begins
1,
0, 1,
1, 0, 1,
1, 1, 0, 1,
0, 1, 1, 0, 1,
1, 0, 1, 1, 0, 1,
1, 1, 0, 1, 1, 0, 1,
0, 1, 1, 0, 1, 1, 0, 1,
1, 0, 1, 1, 0, 1, 1, 0, 1,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1

Crossrefs

Sequence in context: A175192 A088150 A365938 * A307183 A361433 A117568

Adjacent sequences: A117564 A117565 A117566 * A117568 A117569 A117570

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 29 2006

Status

approved