A087748 Triangle formed by reading triangle of Stirling numbers of the first kind (A048994) mod 2.

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

Offset: 0

Author

Philippe Deléham, Oct 02 2003

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
1,
0, 1,
0, 1, 1,
0, 0, 1, 1,
0, 0, 1, 0, 1,
0, 0, 0, 1, 0, 1,
0, 0, 0, 1, 1, 1, 1,
0, 0, 0, 0, 1, 1, 1, 1,
0, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1,
...
		

References

• Brand, Neal; Das, Sajal; Jacob, Tom. The number of nonzero entries in recursively defined tables modulo primes. Proceedings of the Twenty-first Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1990). Congr. Numer. 78 (1990), 47--59. MR1140469 (92h:05004). - From N. J. A. Sloane, Jun 03 2012

Links

• Bill Gosper, Colored illustrations of triangle of Stirling numbers of first kind read mod 2, 3, 4, 5, 6, 7

Crossrefs

Cf. A008275, A008276, A048994, A087755.

Also parity of triangles A049444, A049459, A051338, A051379, A051523.

Formula

T(n, k) = A087755(n, k) = A048994(n, k) mod 2 = A047999([n/2], k-[(n+1)/2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(0, 0) = T(1, 1) = 1 and T(1, 0) = 0; T(2n, k) = T(2n-1, k-1) XOR T(2n-1, k); T(2n+1, k) = T(2n, k-1). - Henry Bottomley, Dec 01 2003

Extensions

Edited and extended by Henry Bottomley, Dec 01 2003