A087755 Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2.

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

Offset: 1

Author

Philippe Deléham, Oct 02 2003

Keywords

• easy
• nonn
• tabl

Comments

Essentially also parity of Mitrinovic's triangles A049458, A049460, A051339, A051380.

Examples

			Triangle begins:
1
1 1
0 1 1
0 1 0 1
0 0 1 0 1
0 0 1 1 1 1
0 0 0 1 1 1 1
0 0 0 1 0 0 0 1
0 0 0 0 1 0 0 0 1
0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 1 1 1 1 1 1 1
		

References

• Das, Sajal K., Joydeep Ghosh, and Narsingh Deo. "Stirling networks: a versatile combinatorial topology for multiprocessor systems." Discrete applied mathematics 37 (1992): 119-146. See p. 122. - N. J. A. Sloane, Nov 20 2014

Programs

PARI

p = 2; s=14; S1T = matrix(s,s,n,k, if(k==1,(-1)^(n-1)*(n-1)!)); for(n=2,s,for(k=2,n, S1T[n,k]=-(n-1)*S1T[n-1,k]+S1T[n-1,k-1]));
S1TMP = matrix(s,s,n,k, S1T[n,k]%p);
for(n=1,s,for(k=1,n,print1(S1TMP[n,k]," "));print()) /* Gerald McGarvey, Oct 17 2009 */

Formula

T(n, k) = A087748(n, k) = A008275(n, k) mod 2 = A047999([n/2], k-[(n+1)/ 2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(1, 1) = T(2, 1) = T(2, 2) = 1; 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